Does a notary stamp make a contract legal?

No, whether or not the contract was notarized is irrlevant when it comes to whether the contract is valid. It is a common misconception that people have, that a contract must be notarized to be valid. Notaries only verify the identity of the person signing the contract.

If you want out of the contract, you should talk to a lawyer about your options under the contract. Most likely there are provisions dealing with breaching the contract, and you will need to decide if the consequences for breach outweigh sitting through the last 5 months of the contract.

Good luck.

A Notary signature only confirms that the party signing is the person who is listed on the documents and that the person signed in front of them.  This helps prevent forgery or later argumetns that the person wasn't the one who actually signed.  A Notary will ask for ID and witness the signature.  A Notary will not sign without ID and shouldn't if the person appears incompetent or under the influence.

There may be many defenses or ways to get out of a specific contract, but, if you signed it, whether there is a Notary signature is not one of them.  There may be vague terms, incomplete or nonperformance by the other side, etc.  Balance the money it might take for an hour of an attorney's time to review with the cost of sticking with the contract or breaking (breach) it.  

A contract is defined as:

contract 1) n. an agreement with specific terms between two or more persons or entities in which there is a promise to do something in return for a valuable benefit known as consideration. Since the law of contracts is at the heart of most business dealings, it is one of the three or four most significant areas of legal concern and can involve variations on circumstances and complexities. The existence of a contract requires finding the following factual elements: a) an offer; b) an acceptance of that offer which results in a meeting of the minds; c) a promise to perform; d) a valuable consideration (which can be a promise or payment in some form); e) a time or event when performance must be made (meet commitments); f) terms and conditions for performance, including fulfilling promises; g) performance. A unilateral contract is one in which there is a promise to pay or give other consideration in return for actual performance. (I will pay you $500 to fix my car by Thursday; the performance is fixing the car by that date). A bilateral contract is one in which a promise is exchanged for a promise. (I promise to fix your car by Thursday and you promise to pay $500 on Thursday). Contracts can be either written or oral, but oral contracts are more difficult to prove and in most jurisdictions the time to sue on the contract is shorter (such as two years for oral compared to four years for written). In some cases a contract can consist of several documents, such as a series of letters, orders, offers and counteroffers. There are a variety of types of contracts: "conditional" on an event occurring; "joint and several," in which several parties make a joint promise to perform, but each is responsible; "implied," in which the courts will determine there is a contract based on the circumstances. Parties can contract to supply all another's requirements, buy all the products made, or enter into an option to renew a contract. The variations are almost limitless. Contracts for illegal purposes are not enforceable at law.