Oral contracts are enforceable in CA, and since you've been performing this one, it would be enforceable even if it violates the Statute of Frauds" because performing it fully would take more than a year.
If you and your lender had an oral contract for a loan which included interest, then interest is collectible. if interest wasn't part of the original deal and the written contract doesn't include it, then your lender won't be able to add it now.
There's also some doubt as to whether that written contract is even enforceable, since it didn't have a payment date, But the fact that you've been making $300 per month payments would mean that $300 per month payments are evidence of an "implied in fact" contract, by your conduct in paying it, even if the written contract doesn't say so and you didn't orally agree to pay the loan back in those monthly payments.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
It is possible that a judge would award interest (known as pre-judgment interest) on the unpaid principal at the present legal rate of 10 percent per year, if the lender decided to take you to court on this loan, even though it does not state any rate in your agreement. However, the arrangement seems rather loose without any set payment terms. Thus, I don't believe that if you are making payments as previously agreed were acceptable, that you would now need to make higher payments, because the lender wants more. It seems to me you are already complying with repayment, as agreed.
Whether the lender can unilaterally charge interest without a court decision is a question that may also depend on whether this person lends to other consumers on a regular basis, thus being subject to the Truth in Lending Act, among many other laws. If they send you a bill with interest, I would send them a letter by certified mail that no interest rate was specified, so you will not agree to pay interest. The problem with the document you signed is that it was very unclear. I cannot state either way if they can demand and receive interest. Ultimately, it is your call if you want to agree with this.