Did u receive u'r I-797 paper?. this will prove that u'r H1 B was filed by the company and if it ever got approved or not. If they are saying that u are not their employee chances are either they have already canceled u'r H1 or just threatening to cancel because you dont have any projects.

your H1 employers are not helpful at all and wont have any feelings for you. Its also not easy to transfer H1 because of the paystubb issues.An H-1B visa holder is considered to be out of status on the day of termination. In order to remain legal in the U.S., the H-1B visa holder must file for H-1B transfer or change of status prior to getting terminated from the present H-1B employment. Some exceptions do exist, however. In light of stricter enforcement of immigration laws and regulations, the chances of getting merciful treatment from the USCIS is remote. Sometimes (underline this sometimes and take it with a grain of salt) the Adjudication Officers at the USCIS have been using their discretionary power to approve H-1B's provided the H-1B petition was submitted within a couple of weeks from the date of termination.

I think you should try to find out if they have actually cancelled u'r H1 and find out ways to transfer back to F1 as early as possible. please also let me know how to go back on f1 once you know it