I took a look through Ableton and it is possible, though potentially more time-consuming depending upon how you have your session set up.
If your edits are clean and each "ooh", "aah", etc. is its own separate region, bring all of the regions into the "session" view as clips. Make sure they are edited with proper start/end times using the start/stop markers in Live's clip view (leave some silence at the end, if possible).
Make sure 'warp' is turned off on all of the cues, unless you somehow used it—this can be done by selecting all of the clips and turning off the warp button in clip view.
Once they are edited, select all of the clips, right click and select "crop clips"—this will make each clip an individual audio file. All you need to do afterward is select all of the clips and drag them onto your desktop or into a folder.
As for the issue of file naming, there are a couple of steps you can take. The name you place on the Ableton clip doesn't necessarily reflect the name that is assigned to the file once you drag it. Check out a really handy piece of software called "Rename It" (or any other batch renaming software). If you work in game audio, you will most definitely find use for batch renaming. It allows you to add, remove, or alter text across hundreds of files by defining simple rules. For your task, I would recommend dragging the files out of Live by category: for instance, drag out the 'oohs' and batch rename them to "ooh_1", "ooh_2", etc... then repeat with the 'aahs'.
MrToBe is somewhat right that this would be somewhat easier in Pro Tools, which has an 'export regions to audio files' function, but we all have our workflows and it's worth making Live work for you if that is your preferred software.
Hope this helps!