Does Halo3ODST come after Halo3

Yes, A. K. A. Halo Recon. It is just an expansion to Halo 3 though, where you play as one of the semi - spartans.

Actually halo3 ODST is set at the same time as halo3 because the war finishes at the end of halo3 and ODST isn't recon its orbital drop shock trooper. You get recon by completing the campaign.