I am making an undead themed campaign, and along the way, players will be able to make pacts with dark creatures, suffuse themselves in necromantic energy, and, most importantly, gain knowledge of the dark arts from pages of a powerful source of dark magic. What are some powers that they could get as a result of this? I want them to be things that any player could benefit from. Necromatic energy from melee weapon attacks wont matter to a wizard, for example. I would also like their to be drawbacks in some way. A penalty to strength as your body begins to take on decay, a frail or jaundiced appearance. Perhaps you begin to shun sunlight? Let me know what y’all have in mind

That is a lot to take in! One thing for spellcasting classes is they might get the option to switch some or all of the damage done by their spells to necrotic damage. At higher levels they might be able to regain hitpoints based on damage dealt. Or lower an enemies' hitpoint maximum until a long rest. Another option for any class would be to use an action to summon necrotic energy from within themselves to cause fear in any enemies within a certain range. For weapon based classes there is the obvious adding necrotic damage to attacks but you could also do some variation on what I said about spellcasting classes. Another option would be to be able to use that weapon to cause a curse effect such as

• Disadvantage on attack roles against you until the end of your next turn.
• Disadvantage on ability checks for an ability of your choice until the next turn. By "your" I mean the player.
• Cannot regain hitpoints until the end of your next turn.

I hope these are helpful! I will send another reply soon about the potential drawbacks to these powers.

Warlock's fiendish vigor, but it decreases your max HP by a half (or other fraction).

Arcane Vigor, but it takes double the hit dice.

If you want it to be useable by any character then the penalty cannot target specific stats (e.g. a wizard doesn't mind losing STR a barbarian certainly does), and it cannot use up Actions (a barbarian or fighter or rogue needs to use their action to attack, whereas a cleric has much more flexibility), and it cannot be specific to spells or weapons.

So...

1. As a bonus action cause fear to creatures around you - drawback = disadvantage on Persuasion checks

2. When deal damage, deal extra necrotic damage - drawback = uses up hit dice.

3. When deal damage, regain hit points or gain temporary hit points - drawback = must kill every day or have hit point maximum decrease.

4. Gain super darkvision/blindsight - drawback = disadvantage on Perception checks when in bright light.

5. Gain Spider Climb - drawback = grow strange wiry hair over arms & legs.

6. Bonus to Sealth/Hiding - drawback = voice become hoarse and whispy.

You could come up with some minor power and hindrance, for example;

Necromance: A pact with dark creatures suffused you in necromantic energy, giving you knowledge of the dark magic while making you sensitive to sunlight. You have Sunlight Sensitivity and Advantage to Intelligence (Arcana) checks to deduce or recall lore about necromantic spells, magic items, and effects of any kinds. You can also Detect Magic (necromancy only) at-will.

An milder alternative to Sunlight Sensitivity could instead be vulnerable to Radiant damage. 

speak with dead is a favorite of mine. It's a very interesting spell which essentially just gives players more NPCs to talk to.  Of course contacting the dead is not without it's dangers  as you could draw the ire of vengeful spirits or darker forces. 

Just include something vague in the description about consequences and  dark forces then you have a huge amount you can do at your discretion.

• curses
• reliving trauma 
• summoning a demon to posses the corpse

Another  trope is bathing in the blood of the young to remain youthful.  Pretty simple to implement you can cast [spell]alter self]/spell] that lasts a day  that involves bathing in some ones blood.  I would also add you can transform your appearance any way you like to that of some one of the same age or older of the blood that you used. However, engaging in a such a monstrous act is corrosive to the soul.  Your true appearance visibly ages a decade each time it's used but your life span is unaffected. Eventually you will appear decrepit and old unless you repeatedly engage in monstrous acts. 

Another is  your shadow having a mind of it's own.  You can cast unseen servant at will  but only when casting a shadow and you can only have one at a time. The servant is visible in light appearing as your shadow and for the duration you have no shadow.  However, your shadow embodies the worst traits of yourself and will act on those impulses when it thinks you won't notice.  If you fall asleep while casting a shadow or leave your shadow unobserved it instead acts on it's own will controlled by the DM. It may escape leaving you without a  shadow until hunted down  at which point it becomes a shadow.