As Alcove said, you can't really do audio post for live theatre. Although, most professional theatres do employ a Sound Designer and indeed the term "Sound Designer" was used in theatre for many decades before it was used in film. The Sound Designer in theatre basically designs all the various sound effects which will be triggered during the performance. In a sense this is more like a sort of "audio pre" than "audio post" though!
Pretty much every audio program for serious or even semi-serious audio (including Audition) will accept wav files (which are of course lossless). Generally therefore you should always assume that wav is the required audio format unless you're specifically asked for something else, which would be virtually unheard to be honest! The format of the wav should be 48kHz/24bit, which should be the format you have recorded all your production sound in. If for some bizarre reason you've recorded at a different sample rate/bit depth you would normally give the audio post peeps your original recordings and let them do the required transcoding. I'm 99% certain that Audition will accept OMFs, there may even be an Audition specific exchange format you can use if you are using Premiere as your NLE. I seem to remember an "Export to Adobe Audition" option in Premiere but like Alcove, I haven't played with either program for quite some time and I might be mistaken.
BTW, be warned, unless the cricket sounds are very sparse and you've been very lucky, the chances are that the audio post guy will only be able to improve your dialogue tracks marginally. Even the very top people using the very finest audio restoration equipment frequently find that the only viable solution for cricket noise is ADR. As I said, you might be lucky depending on exactly where and how often the sound occurs and it's level relative to the dialogue, but don't get your hopes up too high that it can be made to sound unnoticeable or even significantly better (without also destroying the dialogue!).
G
