If I have resided at my residence for 2 years with no lease/rent receipts, what are my rights if my landlord said we had to move?

If you do not have a written lease then you are considered to be a "month-to-month tenant".  Accordingly, absent a lease, you can be asked to vacate the premises upon 30-days notice.  Typically, such notice must be in writing.  Additionally, you are entitled to the return of your security deposit, plus interest, less any legally allowed deductions.

If you do not vacate in a timely manner, you will be considered to be a "holdover tenant" and can be evicted.  You will be held liable for damages as well.

If there is no lease, then your rental is month to month. That means that as long as the landlord provides 30 days or more notice, he or she may terminate your tenancy and ask you to leave. If you do leave voluntarily, the landlord may bring an eviction proceeding against you as well as sue you for "holdover" rent--i.e. for money for each day you stay past when your occupation was over.