Is a contract legal if it has not been notarized? 

Yes, it would be legal without being notaritzed. Nowaday, notarization is almost irrelevant--there are very cases where it is necessary, and a contract is not one of them. Indeed, a contract does not need to be witnessed, either--all that is necessary is for the two parties to the contract to sign it.

However, if this contract only took effect upon your father's death, it may be considered part of or related to his will, and wills do have their own special rules. If it only took effect upon your father's death and you are concerned about it or want to challenge it, you should bring a copy of it in to an estate attorney who can look at it and see if there might be grounds for a challenge. It's not definite there would be, but it's probably worth an hour or two of lawyer time.