Nay verily, I proclaim. If the "220" power in the garage is your typical single phase 240v welder circuit there will be no neutral conductor and thus, no code compliant/safe return path for a 120v load.
If you wanted to break some 120v power off the existing 220v receptacle you would need a small transformer to derive a neutral, which would be cost prohibitive to purchase and install properly.
Just pay a sparky to run a couple extra 120v circuits to the gayrage. It's your best bet..