Buttstomp
When in doubt, buttstomp. I love this. In Single Player while youre in the air buttstomping you are invincible for a second or two. Though its not much, it can save your life in some situations. Though when you buttstomp you cant move side to side (you can but really slow) so if you're buttstomping towards a pit of spikes with a ledge nearby, you probably wont reach it. But everyone can use the buttstomping technique, and its an all around good unconventional weapon. Though its not as useful in mulitplayer (but can produce some nice kills).
Sidekick
I like it better in MP, since its more useful then. In my opinion a sidekick is more useful then an uppercut, but only spaz can do it, so if you're jazz too bad for you.
Uppercut
I rarely use it, except in SP. In mulitplayer you will RARELY kill someone with an uppercut. You have a better chance killing someone with an unpowered, unfast fired blaster than an uppercut. In single player though, its useful for taking out those Raven enemies when they're flying overhead.
Turtle Shell
I like it in SP, since it can help you out from a tight situation. But in MP its basically useless, since you dont see many turtle shells in CTF or battle. Its good in SP, if you find a turtle at least, and can give you 100 extra points as Rad said, but its definately not my favorite.
Lori sidekick move thing
I barely ever played with lori since my TSF is shareware (>(((() but her sidekick like move is ok in Single Player. Never played with her online, though.
Birds
I like these things, sometimes they get annoying though, and shoot down ammo and stuff and make layer 3 look bad, but I like how they are drawn and their style. Never used them in multiplayer, though.

I'd say either buttstomping or Chuck the bird. Though buttstomping is a bit more useful and can help you, I like the bird more since it looks cool and follows you around like a loyal troop or something.
So in Strenght, I'd say buttstomp, but my favorite is the bird, no matter how weaker it is then the buttstomp.

Edit: Forgot about the blue and yellow bird: Its also pretty handy but I find it slightly less handy than the green one,since sometimes it slacks off and leaves enemies behind that hurt me >(

Sometimes the blue bird is more useful, but I like the green one more.