It doesn't say rarites for the colors

If you go by the d100 roles:

• 40% chance of Silver.
• 35% chance of Brass.
• 15% chance of Bronze.
• 10% chance of Iron.

Although there are no solid rules for translating percentage to magic item rarity, if we use the percentage as a gauge, plus taking into account the power of the item in terms of summoned CR 2 monsters and requirements for use, I'd suggest that Silver was Rare, Brass could be Rare or Very Rare, Bronze was Very Rare, and Iron Legendary.

Your instinct was correct, it's rare, rare, very rare, legendary.

For reference:

https://www.dndbeyond.com/magic-items/horn-of-valhalla-silver

https://www.dndbeyond.com/magic-items/horn-of-valhalla-brass

https://www.dndbeyond.com/magic-items/horn-of-valhalla-bronze

https://www.dndbeyond.com/magic-items/horn-of-valhalla-iron

Not sure why they have the different pages, but no links to get to them.

I guess becouse of legal reasons

Quote from Malzorn >>

I guess becouse of legal reasons

 Legal reasons? Like what?

You can see the rarity of a horn type just by mousing over it.

Anyone know offhand if the summoned berserkers are spectral? Corporeal? i.e. Can one move through them or no?

They use the statistics of a "berserker", so its just a regular old humanoid mechanically.  Nothing special about em by RAW.

So, purely hypothetically, what would be the effects of drinking out of one of these?

Considering it's open at both ends that'd require some engineering, but I think in the end you'd sate your thirst. ;) 

It states you must meet requirements or be attacked by the beserkers.  What are the requirements?

The requirements for each type of horn are listed in the last column of the table detailing their respective properties -- basically, the more martial proficiency you have, the better the horn you can use (presumably to gain the spirits' respect).

So... would it be possible to use this to grind exp? If you have plenty of downtime it would be interesting to just, you know, kill a bunch of berserkers once per week. 

Quote from HORRIOR >>

So... would it be possible to use this to grind exp? If you have plenty of downtime it would be interesting to just, you know, kill a bunch of berserkers once per week. 

 Up to your DM. I would say if you summoned them lacking the horns requirements, you could present a case they were legitimate foes, which have the ability to kill and be a challenge in combat, and did try to kill you, making them eligible for combat XP upon defeat.

Though remember you are playing with cheese. After a while and Dm may rule they give no more XP for combat as you have clearly proven they are not challenge for you. Plus, I think it would get boring/drag on, playing  out the same combat encounter, something which you could not just hand-wave if you want to get Xp for it. 

What book is this in? 

What book is this in? 

What book is this in? I'm new to playing. 5th edition. 

If your talking about the item, it's in the Basic Book. (The book which the item appears in the bottom right corner of the item description.)

As for endlessly grinding them, its more up to DM interpretation and limits.

"As your character goes on adventures and overcomes challenges, he or she gains experience, represented by experience points. A character who reaches a specified experience point total advances in capability. This advancement is called gaining a level."----Basic Book, Chapter One.

This would basically be a way for the DM to get out of a endless grind loop if they find it problematic, as they can say the uncontrolled berserk are no longer a 'challenge' for the party to beat, especially if it's become so mundane that it can be hand waved.

Do the Berserkers have their own initiative or do they act at the end of my turn?
Further, do I need to expend any kind of action (action, bonus action, reaction, etc.) to use them? Like the summoning spells (not from Tasha's) require a bonus action to actually use the creatures you summon.

How does dispel work on this?