Should I upgrade #14 wiring on a 20 amp circuit to #12?
The electrical code rewires that ALL of the wiring on a circuit has to be of a size compatible with the rating of the circuit breaker. For a 20A breaker all of the circuit wiring has to 12AWG or heavier gauge.

The problem with the lighting circuit branches at 14AWG is that such wiring is not rated for 20A. If a fault or short circuit should occur in the lighting section of the circuit that wiring can overheat and could even cause a fire. 

The fix for this problem can take one of two forms:


Replace all of the 14AWG branch circuit wiring with 12AWG wiring.
Consider equipping the wiring entry point at your detached garage with an entry point distribution box that can support multiple breakers. Feed the incoming power line in through a 20A breaker. Then add load breakers as needed to the box to feed down stream circuits. Use a 20A breaker for the existing 12AWG wiring that goes to the garage door outlet. Reroute the 14AWG lighting circuit wiring to the distribution box and connect it to a 15A load breaker. Finally add another 20A load breaker and 12AWG wiring that routes to the electrical box(es) where you want to add the additional outlets.


Note that if you choose to go the route of item #2 the existing 14AWG wiring for the lights may not be long enough to reach to the distribution box. If you have to add wire make sure to connect the added wire to the existing wiring inside an approved electrical box that remains accessible.