Home electrical question.

Check to see if there are 3 wires to the 220 outlet or 4.
If three, there should be two hots and a neutral, thus no ground. Althogh the neutral is eventualy tied to the ground, it would be nice to have a ground. You could use one of the hots as a ground if you move it from the breaker to the ground bar. The color will be wrong though.

I would recommend a transformer based system to drop the 220 to 110, this will further isolate the line. Run that to a dedicated subpanel and run your system off that.

If it's installed correctly, that 220V line is dedicated to the dryer only. If you want to use the line for 120V and you say it's expensive to run a new seperate line, you may be out of luck if it's a 2-wire line since a neutral is required for each 120V leg that you use as a circuit, as well as a ground. The neutral would have to run back to the main panel and be grounded there with the ground wire and water pipe. So it's just like installing a new circuit from the main panel.

However, if the dryer line is a 3-wire BX or 4-wire NM, you can use this as a feeder to a new subpanel. The 220 volt lines, the neutral and ground (wire or armor) is a legal feeder to the subpanel since they run straight to the main panel and the neutral and ground are bonded there.

The new subpanel must have either a main breaker or a disconnect switch upstream that cannot have an amperage rating higher than 80% of the existing dryer wire. The neutral bar in the new subpanel MUST BE ISOLATED from the subpanel (remove the bonding screw) because you can only ground at one point in an electrical system. Install breakers in the subpanel with normal wiring to the outlets and you're done.

This is a guide, your electrician overrules all of us.