Is there any rule that says that a Magic rod cannot be used as a melee club?

If so, then the Shillelagh spell should be able to be cast on it. 

I see no reason why a Warlock with a Rod of the Pact Keeper could not use it as a club and then apply the Shillelagh spell to it if they have access to the cantrip.

Ultimately, it's up to the DM, as it is an "improvised weapon," but many like me, especially if approached beforehand about the plan, would allow it. 

Is there a rule that say you can’t use it as a club? Not that I’m aware off and I’ll second the reference to an improvised weapon

i do rule that spells do what spells say they do, so is the item a “club” for the purpose of Shillelagh, or is it an improvised weapon? 

if it is a club, then yes

then what about a Rod of the Pact Keeper? Can this be used with Shillelagh - if it’s a “club” then yes and the bonus from the rod is for spell attacks

So what about the new True Strike, does this then stack with Shillelagh and new True Strike?

I‘m thinking it does, do you gain a benefit from mucking around with multiple spells like this? Maybe not

A rod is not a weapon, unless it's description says so (eg rod of Smiting). They are frail like wands. You strike something they are destroyed.

Not necessarily.

Quote from MPA >>

A rod is not a weapon, unless it's description says so (eg rod of Smiting). They are frail like wands. You strike something they are destroyed.

 Rod can refer to a long list of things. I doubt that's the one they're going for in an RPG game, though. I rather suspect it's this one: 

The Rod

• The rod was a short, sturdy club or stick, often carried by shepherds to protect their flock. It was used as:
  • A weapon: To fend off predators like wolves or thieves threatening the sheep.
  • A tool of discipline: To correct wayward sheep gently or symbolically enforce authority.
  • A symbol of power and authority: Representing God's protection and ability to defend His people from harm.

So can magic staffs, like a Staff of Fire, be used as quarter staves for melee purposes, even though it is not expressly mentioned within their descriptions?

Or are they just improvised weapons by that logic?

There isn't many magic staffs that have actual weapon attributes listed in their descriptions. I would say that they are just generally magic quarter staves without melee bonus' applied as attributes.

Being able to apply Shillelagh  or cast Magic Weapon on a Staff of Fire seems perfectly logical to me.

From AD&D 1e's DMG:

RODS, et al. (Including Staves and Wands) (111.D.)

Rods are about 3’ long and as thick as your thumb. Staves are about 5’ or 6‘
long and as thick as a young sapling, i.e. about an inch and a half at the
base, tapering to an inch at the tip, although they can be of nearly equal
diameter throughout, knurled, etc. Wands are 1 1/4’ long and slender. 

Rods are fashioned from metal, strange wood, ivory or bone. They can be plain
or decorated and carved, tipped or not. Staves are typically fashioned of
wood, often carved, usually metal bound and shod, and likely to be gnarly
and twisted. They can be unusual or appear to be ordinary. Wands are of
ivory, bone, or wood and are usually tipped with something - metal,
crystal, stone, etc. They are fragile and tend to break easily.

I presume those descriptions are still the case unless it has been retconned/changed in later editions. 

Quote from MPA >>

From AD&D 1e's DMG:

RODS, et 01. (Including Staves and Wands) (111.0.)

Rods are about 3’ long and as thick as your thumb. Staves are about 5’ or 6‘
long and as thick as a young sapling, i.e. about an inch and a half at the
base, tapering to an inch at the tip, although they can be of nearly equal
diameter throughout, knurled, etc. Wands are 1 1/4’ long and slender. 

Rods are fashioned from metal, strange wood, ivory or bone. They can be plain
or decorated and carved, tipped or not. Staves are typically fashioned of
wood, often carved, usually metal bound and shod, and likely to be gnarly
and twisted. They can be unusual or appear to be ordinary. Wands are of
ivory, bone, or wood and are usually tipped with something - metal,
crystal, stone, etc. They are fragile and tend to break easily.

 Not this edition, not relevant to this edition's rules.

Quote from 1naughtypilot >>

So can magic staffs, like a Staff of Fire, be used as quarter staves for melee purposes, even though it is not expressly mentioned within their descriptions?

Actually, that's covered in both the PHB and the DMG. In the DMG, "Unless its description notes otherwise, a staff can be used as a nonmagical Quarterstaff and an Arcane Focus."

It's a common houserule that rods can be used as clubs, but it's not RAW.

Quote from kenclary >>

Quote from 1naughtypilot >>

So can magic staffs, like a Staff of Fire, be used as quarter staves for melee purposes, even though it is not expressly mentioned within their descriptions?

Actually, that's covered in both the PHB and the DMG. In the DMG, "Unless its description notes otherwise, a staff can be used as a nonmagical Quarterstaff and an Arcane Focus."

It's a common houserule that rods can be used as clubs, but it's not RAW.

 I understand that, but I was trying to make a point.

Here's another example using a Rod of Alertness

AD&D 2nd Edition Version's wording:

"Rod of Alertness: This magical rod is indistinguishable from a footman's mace +1. It has eight flanges on its macelike head. The rod bestows +1 to the possessor's die roll for being surprised, and in combat the possessor gains -1 on initiative die rolls. If it is grasped firmly, the rod enables the character to detect alignment, evil, good, illusions, invisibility, lie, or magic. The use of these detect powers does not expend any of the charges in the rod.

 D&D 3E wording:

This rod is indistinguishable from a +1 light mace. It has eight flanges on its macelike head. The rod bestows a +1 initiative bonus. If grasped firmly, the rod enables the holder to detect evil, detect good, detect chaos, detect law, detect magic, discern lies, or see invisibility. The use of these powers can be done freely with the rod, each different use taking a separate standard action.If the head of a rod of alertness is planted in the ground, and the possessor wills it to alertness (a standard action), the rod senses any creature within 120 feet who intends to harm the possessor. Each of the flanges on the rods head then casts a light spell along the direction it faces (usually north, northeast, east, southeast, south, southwest, west, and northwest) out to a 60-foot range. At the same time, the rod creates the effect of a prayer spell upon all creatures friendly to the possessor in a 20-foot radius. Immediately thereafter, the rod sends forth a mental alert to these friendly creatures, warning them of possible danger from the unfriendly creature or creatures within the 120-foot radius. These effects last for 10 minutes, and the rod can perform this function once per day.Last, the rod can be used to simulate the casting of an animate objects spell, utilizing any eight (or fewer) objects located roughly around the perimeter of a 5-foot-radius circle centered on the rod when planted in the ground. Objects remain animated for 10 minutes. The rod can perform this function once per day.

DnD 2024 Edition

This rod has the following properties.

Alertness. While holding the rod, you have Advantage on Wisdom (Perception) checks and on Initiative rolls. Spells. While holding the rod, you can cast the following spells from it:

• Detect Evil and Good
• Detect Magic
• Detect Poison and Disease
• See Invisibility

Protective Aura. As a Magic action, you can plant the haft end of the rod in the ground, whereupon the rod’s head sheds Bright Light in a 60-foot radius and Dim Light for an additional 60 feet. While in that Bright Light, you and your allies gain a +1 bonus to Armor Class and saving throws and can sense the location of any Invisible creature that is also in the Bright Light.

The rod’s head stops glowing and the effect ends after 10 minutes or when a creature takes a Magic action to pull the rod from the ground. Once used, this property can’t be used again until the next dawn.

Clearly the Rod of Alertness was considered a useable weapon for 20 years of D&D before 5th edition came along.....so I think I'll just consider it one now as well.

I think I would rule it based on what the rod is actually made of.  if the rod is made of wood, then I'd probably allow shillelagh to work with it.  if it's metal or bone or whatever else, then I don't think shillelagh should apply to it.  other than that, I don't see why it wouldn't be statted like a club in combat, unless it seems too fragile for combat.

3.5 did have a generic rule that many (not all) rods could double as clubs or light maces. But 5e has no such rule, and even if it did, whether you could Shillelagh a rod would depend heavily on the exact text of such a hypothetical rule.

The closest thing to a rule about that which I can find is in the PHB in the section on improvised weapons:

"Often, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the DM’s option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus."

RAW, you can't. RAI, you can't. By that logic, there is no rule saying that you can't wear a cloak as a set of plate armor. It probably isn't game breaking, but your question makes no sense.

I would say no.  A rod is not a club and cannot be used as one.  arcane staves are explicitly called out as being able to be used as a quarterstaff.  No such provision is made for a rod.  So, by omission, it cannot be used as a club.  Also, Shillelagh cannot be used.  It does what it says it does.  It works on clubs and staves.  Not improvised clubs (which a rod could be counted as).  They not even explicitly wood.