If you had an agreement that amounts to a contract, it is binding even if it was informal. However, if your agreement was not in writing, it might be hard to prove.
You can easily prove that you transferred money to the other party. But can you prove that it was a loan an not a gift? And even if it is agreed to be a loan, if no repayment time was specified, what says that the debt is due now? Was the agreement really for a loan repayable on demand? The court would have to determine what your real contract was, or what contract can be implied from the actions of the parties.
Also, if you are in a common-law jurisdiction, there could be a question of what consideration there was for the loan. Without consideration, there is no valid contract in such a jurisdiction. Perhaps a promise to repay could be treated as sufficient consideration.
Small-claims courts do deal with unclear verbal contracts on a regular basis, but the outcome will depend on the facts of the case, and on the details of local law. It might be wise to consult a local lawyer with small-claims experience. A single consultation should not be too expensive.
In response to comment If the "written binding agreements" include a statement from the other person that this is a loan, and a promise to repay it, you are in a stronger position than I had thought from the original question. The question for the court would be, since there was no due date agreed, what is a reasonable date to impose. The court might treat it as a loan repayable on demand, or specify some particular date for repayment.
