You are en emperor of a space empire and you have various races in the empire (I look for pretty standard ones, so no energy beings and such :)). I wanted to categorize them into bigger groups, like you conquered a planet and there is a "Humanoid" race (without specifying what kind).

I thought of these:

Humanoids - terrans and all races from StarTrek :D

Insectoids - ants, bugs and other hive type beings

??? - bird like

??? - cat/bear/wolf like (agile, aggressive)

Octopoids - octopus like, tentacles and the like

I also look for names for the "???".

You need a recipe here; one could be:

a) find a term, plus a few alternative ones that describe the category (reference species, most recognizable feature in a body/behaviour-wise sense, etc)

b) get a good latin online dictionary, put it in there, try your alternatives, until you find a translation that sounds good and might be known to your user (you dont want them to grab an online dictionary either during gameplay, to reverse-engineer your namefinding process)

c) slap "-oid" behind it

d) google it if it is a thing, if yes - done, if not - maybe done, or find another word, up to you

for your given examples, this could result in:

avianoid (http://memory-beta.wikia.com/wiki/Avianoid - star trek was quicker)

avioid (sounds like a typo)

rapaxoid (sounds nice, seems to be unknown)

carnivoroid (seems to be a thing in biology, though I didnt really read the papers I found; might as well be proposals to diss the term:) )

If you want to group cats, bears and wolves together they would be carnivores (thats their RL classification, order carnivora).

Also put reptilians, people like reptilians.

Others can be crustaceans (similar to insectoids, but underwater), fish/whales, plants, fungi, worms, other kinds of mammals.

I still look for a few of these.

"worms" - how to call such race?

Also I have a race of mindless symbiots/parasitic ones, looking for a name.

Birds - Avians
Bears - Ursa
Wolves - Lupians

Should they all be bipeds and display bilateral symmetry?

No... Not necessarily.

Well, maybe less standard/latin name for these? Something still similar and giving the impression of the terra animals but sounding more alienish (especially the Wolves).

Looking at your previous list, your names seem to follow a standard "Latinish" naming scheme; if you want names that sound more alien, do you perhaps want those changed as well? After all, "insectoid" and "octopoid" aren't far off from "lupine", "ursine" and "avian"...

As to finding new ideas for creatures, it's a little cliche, perhaps, but have you considered looking at deep-sea creatures for inspiration? There are some awfully weird-looking creatures down there, and you may find some interesting designs for aliens. Another potential source for ideas might be prehistory--especially the very early stages of life. For a few examples, take a look at this, this and this.