Normally you would read your lease to verify the terms and conditions around fees and deposits.
Most pet deposits are non-refundable.
As for the security deposit .... you may be correct and due a return of your deposit .... less any damages where he can document he paid for something.
Why would you be entitled to a relocation check?? (How have you been wronged?). You are a renter .... rentals are not permanent. If you had a formal written lease in place .... then you would have a case stating you planned to be in the unit until a specific date. The new owner could then choose to honor the lease or settle with you to vacate early.
Since you lived on a verbal agreement, you have very limited recourse, as the standard assumption would be that you are a month to month tenant ..... which means with 30 days notice the new owners can require your departure.