There are several versions of the ODST now, so you'll have to be a little more specific as to which version you're curious about. We're all probably assuming you mean the game version from Halo 3: ODST, but just to illustrate my point, the current variations of the ODST are as follows:
-Halo 2 game version
-"Landfall" Halo 3 short film live-action version (by Weta)
-Halo 3 game version
-High-Def Bungie pre-production 3D model sent to Legacy Effects
-"We are ODST" short film live-action version (by Legacy Effects)
-Halo 3: ODST game version
-and now the Halo Reach live action teaser version (variants of LE version)
All sport different looks and different possibilities for undersuits.
For the Halo 2 game version, you're probably looking at dark urban camo supplemented by additional dying with black dye to make it even darker.
For the Halo 3 and Halo 3: ODST versions, there is so little of the bottom-most layer of the suit showing that you're best bet would probably be just some plain black pants and a black underarmor shirt. Perhaps bleaching them slightly to lighten them up so they aren't 100% black.
For the Landfall (Weta) version, you see a bit more of the undersuit, but not much more. But same deal as above, black pants (perhaps BDUs) with a black underarmor shirt. With the Weta version you can actually see the shirt is form-fitting around his arms in the armpit and elbow areas.
For the Legacy Effects "We are ODST" version, you're looking at two different versions: a dirty brown jumpsuit and a dirty OD green jumpsuit, both with removed collars.
For the new Legacy Effects Halo Reach teaser, it's woodland digital camo coveralls, specifically, and not a flightsuit. This one has the collar still attached (and righteously popped, I might add. lol). I have this on order, actually, so I can post pictures later when it arrives.
Here are some pics of the costumes I built, which are replicas of the Legacy Effects "We are ODST" short film. Note that in the bottom pic, each costume sports the different color flightsuit. Front trooper has the dirty OD green, and back trooper (me) sports the dirty brown.