I am sorry to learn of this situation.
You actually DO have a contract, albeit an oral one. This oral contract is supported by the circumstantial evidence of your receipts for materials, correspondence with the contractor, permits with the code department, and with any other third parties. It is also supported by your own testimony.
You can sue the contractor for breach of contract, the measure of damages is going to be the cost of hiring another contractor to come in and perform the work to complete the project as agreed upon.
Short of filing a lawsuit, you can try to mediate the dispute with them - contact your local bar association and request referrals to mediators, a third party neutral can often help you reach a mutually agreeable resolution. Use the bar association's referrals to contact a mediator or two, the mediator will then contact the other party to set up a mediation session, and you can go from there - hopefully resulting in a formal or written settlement agreement, and save yourself the time and expense of litigation.
The title question issue s a little harder for me to help you with as title insurance is a contract between you and the carrier, and different policies provide different types of protection. I would recommend speaking with a local civil litigation attorney to help you with this claim.
You can find local attorneys using the State and local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).