I need to install an oven that is 208v single phase but draws 96 amps. The panel is about 120 feet away and is only 150amp. Is this possible given the fact there is already (14) single pole 20, (2) two pole 20, (3) two pole 30, and (1) two pole 50. Also, do you think a 3/3 MC is acceptable?

Since this is obviously a commercial setting, why not let someone with the knowledge and experience handle this job?
Someone doing such an installation should not have to ask these questions.

FTR, no way I'd feed this oven from that panel. Unless most of those breakers are not being used at all.

I assume this is not for your dwelling..correct? Is this for a business?
Do you have the maximum annual or monthly demand load on this 150 ampere panel?
(This information is required for permit approval)
#3 AWG is too small for a 100 ampere overcurrent device. You will need to use
#1 AWG cable based on NEC 110.14(C)(1) and 310.15(B)(16).

It's unlikely that your service can handle this additional load. Maybe a smaller oven or a service upgrade is needed. When in doubt call in a professional.
This is a DIY room with para-professionals.