Electrical – Can i use the old electric water heater electrical supply wire to power new outlets

Yes, it can, but for normal 120v outlets, you'll need to swap the 240 volt/30 amp breaker for a 120v 20 amp, I suggest a "DUFI" if available for your panel. DUFIs are industry slang for Dual function breakers. They actually do 4 things: 1) Normal over-current protection, 2) Ground Fault protection, 3) Series arc fault protection and 4) parallel arc fault protection. You'll need to get filler plate to block off the space since the 120 v breaker will be taking 1 slot whereas the 240 took two.

Depending upon your jurisdiction, only GFCI may be required for outdoor outlets. But AFCI isn't a bad thing. Others here (with more knowledge than me) favor using GFCI breakers in panels rather than GFCI outlets, the reasoning is they are protected from the weather, by being installed in a panel and last a lot longer.

OK, that aside said, moving on: At the box where the old water heater was, run 12/2 from there to your outdoor outlets. Use high quality outlets, not $.79 cheapies. You'll install the white wire that is now the neutral to the GFCI breaker (assuming you go that route), and the white pig-tail from the breaker to the neutral bus bar. If you choose to use a GFCI outlet "first in line" for your outdoor outlets, you'll need to move the white wire that was formally connected to the water heater breaker to the neutral bus bar. Mark the 10ga wires with a tag saying there is 12ga as part of that circuit. Any decent electrician would probably realize that, but a future homeowner might not. No penalty for clarity!

I'd like to see a pic of the inside of your main panel to see exactly what we are dealing with. Brand and age of panel also helps. Based on that, I may update my answer.

CAVEAT: What I responded with is what is a "typical" install, if you have something more unique, your mileage my vary. Again, shoot us a pic of the innards and we can be more sure.