Tetryon has a chance to reduce the target shields, and plasma has a chance to de damage over time to the hull. Auxiliary power modifies the effectiveness and/or duration of certain powers for example but not limited to powers like auxiliary to SIF or tykens rift.
For space, different weapon types have different procs, to find out what it is, look for where it says "2.5% chance to apply...."
Hers a quick rundown though
Phaser - Disable 1 subsystem temporarily
Disruptor - 10% energy weapon resistance debuff
Tetryon - Pathetically small shield drain (just stay aways from Tetryon really)
Polaron - Drain power levels
Plasma - Add DoT (damage over time)
Anti-proton - Increased crit severity (crits hurt more)
Remember, thats all on a 2.5% chance, while it happens more often than you might think, its not something to rely on too much.
Similar story for projectiles but I can't remember those off the top of my head, its all in the tooltip anyway.
[Acc] Hit them more often
[Dmg] More damage
[CritH] Higher chance of critical hits
[CritD] Crits do more damage
[Borg] Chance to add DoT to Borg enemies
Auxilliary power wil increase the damage or effectiveness of most science powers and a few engineering powers (Auxilliary to Structural Integrity Field, Auxilliary to Inertial Dampeners etc), it also very slightly raises stealth (cloak) detection and resistance to certain Sci powers (might be mistaken on that last one).
I think thats the short version, probably missed some things but someone will be along to fill in the blanks shortly.