please help - H1B visa transfer difficulties

[midnight55]

I have a H1B visa and am about to start the process of applying to transfer to a different employer, as me and my employer have mutually agreed to end job,although they initiated this proceeding. My current employer told me that i will work for them till july 31st, i was told i had to hand in written resignation by yesterday and handed in a resignation stating that i will provide my last date of work in a week as it is dependent on my starting date at a new job. They told me that i cannot leave before end of july as they hold my visa and will not release it until July. (new job starts beginning of June)

I have an offer letter from them stating if i leave before contract is up i will be responsible for repaying visa costs - unfortunately for them i did not ever sign a contract as they never gave me one (they even emailed me a notice saying they should probably write up a contract but there prety bad at things like that' - but surely if they initiated the move to end the contract i would not be responsible for this.

Please help - i need to think of my new job, not my old one....

On another note, my employer was my co-buyer on my car and they have asked me to remove their name. If they agreed to do this, legally are they not stuck with this. i have option to refinance my car, to remover name but not with a very good deal..