Short answer: You cannot play ODST Firefight online via official matchmaking. The mode was designed exclusively for local split-screen (up to 2 players) and system-link LAN (up to 4 players). No dedicated servers or online matchmaking were ever implemented.
Community projects (like Halo Online derivatives or Xenia emulator netplay) have attempted to enable online Firefight. They are:
Local split-screen and system-link LAN still work perfectly on original hardware or MCC. For online co-op survival, Reach remains the definitive way to play.