I agree with Ray. But of your four suggestions, the one that sounds most natural is (4).

Some pronouns like HIS, HERS, MINE and OURS are called Absolute Possessives. They can stand alone without nouns. For example, "the house is MINE". The word MINE is not beside the word HOUSE. Other pronouns like MY and HER need to be attached to a noun. For example, "My house" The word MY is beside the word HOUSE. In three of your examples, you have used pronouns without attaching them to nouns. 1. This is my (you need a noun here) and Jane's house. 2. This is my (you need a noun here) and her house. 3. This is her (you need a noun here) and my house. In the 4th example, you have used ABSOLUTE POSSESSIVE PRONOUNS properly. However, a native speaker would say "OURS" or possibly, "The house is hers AND mine". (Pausing before and stressing the word AND to make a point) Hope this helps

Another alternative is to say, "This is my house and Jane's." Compound possessives can be awkward so we usually avoid them by simply saying "our".

The correct way our house, why do you need to avoid this? It is perfectly natural. The other way would be to say 'This house belongs to Jane and me.