can a company sue me if I am making some kind of payment.

Yes, they can.  If the debt is due, then it is due in full, and the creditor does not have to accept payments, unless it has agreed to do so.

I am not familiar with Oklahoma law, but I've never heard of any law in any jurisdiction which would prevent a creditor from suing you if you are making any payment on the debt, unless you had an agreement with the creditor to that effect.  As for the second part of your question, as I understand it, you had an agreement with the dealership, a third party, that it would pay the debt.  This agreement may be binding on you and the dealership, but, unless the creditor was a party to the agreement, it doesn't affect your obligation to the creditor.  In other words, you and I can agree that, in exchange for your car, I'll make all further payments on the car loan.  If I don't pay, you can sue me, but you are still obligated to pay the lender.  Your agreement with me doesn't change anything about your agreement with the lender, unless the lender is party to the agreement with me.