That depends on the oral agreement. An argument could be made that they were change orders or modifications to the original contract. An argument could also be made that these were separate contracts. Without more detail regarding the oral agreements it is hard to say. However, if you tell us what the problem is that you are facing, we may be able to answer you more effectively.
More than likely, the extra work would be considered part of the original contract. But if the contract is as you describe, then it is not in compliance with the Home Improvement Contract requirements. You may want to contact the CSLB about filing a complaint against this contractor. You should consult with an attorney that has experience with construction issues to make sure your rights are adequately protected.
I have agreed with the prior answers provided, and I believe it is most likely that this additional work will be considered a change order to the original scope of the work, even though you requested 'separate bids' and sought other bids. It is not unusual for such additional work to be the subject of additional competitive bids, particularly where the existing contract does not contain any terms to prohibit another contractor from performing work on the job.
More important, however, is to understand the reason for your inquiry, which will shape the answer you receive. As noted in a prior answer, the contract(s) may not meet the requirements for home improvement contracts in California, and may subject the contractor to liability for this apparent violation. Are you attempting to terminate his performance and hire another contractor to finish the work? Are you concerned about not have a written agreement for the additional work? Is there a dispute about the payment terms and progress payments? There are many potential issues and your question does not provide enough information to permit a more thorough answer.
If you are having a problem with the contractor, I strongly encourage you to consult a local attorney regarding the issues. I would be happy to discuss this with you, and there are many competent local attorneys for this as well.