How many passengers allowed in a car in Oklahoma, USA?

The only likely legal limitation is that there must be a seat belt for every passenger.

Some states only require seat belts for passengers in the front seat, or under a certain age (such as 13).

But to be safe, make sure every passenger is buckled in, and you will have no problems anywhere in the U.S.

As per the NHTSA summary, the number of occupants in the rear seat cannot exceed the number of available safety belts. Including the citations of the relevant laws on pages 19, 29, 33, etc.

The state of Oklahoma does not require rear-seat passengers to wear seat belts:

All drivers and front seat passengers ages 13 and older must have a safety belt properly fastened about his/her body at all times while the vehicle is being operated.

This would imply that you can legally pile four people into the backseat and/or the cargo area. The only other laws I've been able to find concerning passengers and where they can ride either apply to larger vehicles (with a seating of 15 or more) or concern whether passengers can ride outside the passenger compartment (short answer: in the bed of a pickup truck or in a parade, otherwise no.)

If you are passing through any other states on the road-trip, the Governors' Highway Safety Association has a good collection of summaries of each state's traffic laws, including seat belt laws.