TX, like every other state, has "common law" authority that governs oral contracts, and nboatloads of court-made law dealing with the enforceability of most oral contracts and contracts "implied in law" by the parties' conduct. A contract may be either written or oral, unless the contract is required to be written by law, for example, a sale of real estate. An oral agreement is just as binding and effectual as an agreement in writing.
In TX, the elements that are generally required to create an enforceable contract:
(1) An offer;
(2) Acceptance in strict compliance with terms of the offer;
(3) A meeting of the minds with respect to both the subject matter of the agreement and all of its essential terms;
(4) A communication that each party has consented to the terms of the agreement;
(5) For a written contract, execution and delivery of the contract with an intent that it become mutual and binding on both parties; and
Angelou v. African Overseas Union, 33 S.W.3d 269, 278 (Tex.App.-Houston [14th Dist.] 2000, no pet.).
To constitute a valid contract, the minds of the parties must have a "meeting of the minds" regarding the subject matter of the agreement, and as to all of its essential terms; and all of them must agree to the same thing in the same sense at the same time. Solis v. Evins, 951 S.W.2d 44, 49 (Tex.App.--Corpus Christi 1997, no writ). Their consent or agreement must comprehend the whole proposition, and the agreement must comprise all the terms which they intend to introduce into it. Id. There is no contract where material terms are left for future adjustment, or are not agreed upon. Id.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't 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.