What kind of effect did this Pokemon have during its time in the 5th Gen NU Metagame?
Absol possesses the strongest priority attack outside of Ubers in it's STAB sucker punch, as well as Pursuit, Nigth Slash, and coverage options like Superpower, Megahorn, and Psycho Cut. Absol alone made frail ghosts and Psychics a liability to be used, as a pokemon (lets use Haunter) had 2 options: Switch and most likely die, or stay in and still take a giant chunk of your health, and probably die. Even frail sweepers such as Cinccino were OKHOed by a powerful sucker punch. Absol was slow, but priority made up for that. Because of it, Fast Fighters like Emboar and Sawk that could comfortably take a Punch from him and OHKO rose.
What were its main roles when it was/is used?
Absol had 2 main sets: a swords dance set, and an all out attacker set (and a scarf set too i guess). The swords dance set was the most threatening, but Absol did suffer from 4MSS, but it did obtain perfect coverage anyways. 4 attacks was more dangerous from the start, but it had more counters as Absol couldnt boost its attack. It was mainly used as a trapper, Sweeper, and a cleaner with Sucker Punch.
What caused it to have such a significant impact? (Think Movesets, abilities, base stats, etc)
Absol has the strongest Priority IN THE GAME. Frail choice users such as Haunter and Mesprit that couldnt take a Sucker Punch were hard pressed to beat Absol. It's abilities, Pressure and Super Luck, arnet that great, but Super Luck with it's high crit moves is fun with hax. The rest of his stats are low, but when you ware that strong thats ok.
How would you deal with this Pokemon when you are team building/battling it? (checks, counters, etc)
Strong fighting types like Emboar (who moved up the same time as absol) were the best ways to deal with Absol. Pokemon that can play mind games with Absol and have to cause massive prediction with either using a status move to make Sucker Punch fail, or Attack and kill absol, also were good. Some scarfers, but they had to be able to take a powerful sucker Punch. Faster Priority was a big one (Linoone is an example) can punch through Absols low defenses.