Can salaried employees who are exempt from overtime also receive standby pay? If so, are they entitled to overtime if they return to work during off hours?

The employees may receive standby pay. You can pay them overtime if they are required to return to work, but you are not required to do so.

29 CFR 541.604(a) allows an employer to provide an exempt employee with additional compensation without losing the exemption or violating the salary basis requirement, if the employment arrangement also includes a guarantee of at least the minimum weekly required amount paid on a salary basis. Thus, for example, an exempt employee guaranteed at least $455 each week paid on a salary basis may also receive a 1% commission on sales as additional compensation.

29 CFR 541.604(a) also states that the additional compensation may be paid on any basis without jeopardizing the employee's exempt status (e.g., flat sum, bonus payment, straight-time hourly amount, time and one-half, or any other basis). This compensation may include paid time off.

It is important to note that neither standby pay nor overtime pay is required under the Fair Labor Standards Act (FLSA) for exempt employees.

You should also make sure to check state overtime laws, if you decide to pay the employees overtime. State laws may supersede federal laws governing overtime if the state law is more advantageous to the employee.