If the garage has accessible outlets (you can easily plug something into them) it has to be either a GFCI or down the line from a GFCI. Your garage door opener receptacle (depending on its location) may not fall into this category. All other accessible outlets do.
Some flourescent lights will malfunction without a proper ground in place. Keep that in mind.
If you want to do things right, just install new runs of 12/2 Romex and replace the existing wiring from the panel with 12/2. Have the first outlet on the line be wired with a GFCI receptacle. Otherwise things may get a little messy in how you ground that run.
If the wiring is all 12ga, you can also then replace the breaker with a 20a SP breaker. Look on your panel for the manufacturer to get the correct brand of breaker. For the most part, Murray, Siemens, Cutler-Hammer, and a few other manufacturers are pretty much all interchangeable. Square D and GE are two brands that get messy matching up sometimes.
Also wondering, why on earth do you have 3 switched outlets? You're going to just plug in the lights instead of hard-wiring I assume?
EDIT: If you're going to ground the line to a water pipe, you are NOT going to use 14ga wire. You're going to either run 12 or 10ga wire (THWN I believe) to a metal water pipe within the first 5' of it entering the house. Either that, or you're installing a new ground rod.
EDIT 2: New THHN wire (most commonly sold single conductor at improvement stores) is going to be THWN rated so you'll be fine using that.