Can my employer give me cash or gift card for working off the clock
No, they can't do this: if an hourly employee works, the employer must track his or her time and must pay him or her for all hours worked, including paying overtime for any hours worked over or past 40 hours in a workweek. That's the law (e.g. the Fair Labor Standards Act, or FLSA) and employers have no discretion in it. If they don't pay you  as required, you could file a complaint with the department of labor; and legally, they may not terminate you for insisting on your rights under the law, and if they do, you could again, file a labor department complaint.That's the law: you have to decide if what they are offering you is fair or reasonable and, if so, whether it would be better to accept than to file complaints and deal with a possible legal action. You have legal rights, but do the thing here that works best for you.