So I have an undying warlock in a campaign I play in and I want to know. Is possession a spell, attack, or nether of those?

Possession is an action some monsters have, like Ghosts. I am not aware of any player accessible option that achieves a similar effect.

As a Warlock much of what your character can do is determined by what spells you have learned. I would suggest looking at spells under the Warlock spells in the basic rules - https://www.dndbeyond.com/sources/basic-rules/spells#WarlockSpells

Don't worry about memorizing every spell in that list. Just skim through it enough to decide which spells your character learns and then focus on understanding how those work.

I was more so asking to see if the Among the Dead feet would be activated by a ghost using possession

I’d rule possession is not effected by Among the Dead. That applies only to attacks or harmful spells.

Possession is not an attack, since there’s no attack roll. It’s also not a spell. And it’s not inherently harmful, in that it does no damage to you. 

thanks for the info for future reference, but I have a question. If the ghost were able to gain the information from the target, skip the cooldown, and gain access to their abilities. Would it be then considered harmful? (Dm made a broken ghost)

The term “harmful” is not defined in RAW, so it’s up to a DM ruling. Typically, it refers to taking damage, but it doesn’t necessarily have to. 
In this case, sounds like your DM homebrewed their ghost. When that happens, all bet are off. Really, a DM can freely change a monster’s powers without it being a full-blown homebrew, and make any creature do whatever they want. There’s a point where it’s a jerk move, but that’s why a good DM will work to build trust before they go off script.