Overkill T1 adds +1 to the kill tally whenever you kill an enemy. Overkill T2 adds an extra +1 to the kill tally for every 100 max levels you have, and T3 adds +1 every 50 max levels. Its only use is to run through Stages faster to grind Ascension Shards.
Sniper T2 doubles your damage if your crit chance is over 100%. No clue what Sniper T3 does exactly though...