</font><font color="blue" class="small">( My compressor only has places for 3 wires. I was told by the "expert" at Home Depot to wire the green and white wires together and put them on the green spade.)</font>
That expert is wrong. Very wrong.
The white (neutral in the us) and green wire (ground in us) should be connected one place and only one place and that is at the service entrance panel.
I am not an electrician but I seem to recall the NEC specifically prohibiting using dual mode 120/240 outlets for 240 only appliances. I have no clue why, but I have been told that it is prohibited.
If you want to do it right, then I would suggest the same thing that the others have recommended, running a dedicated 240/15 or 240/20 outlet for the compressor.
On the other hand, let's remember who wrote the NEC and what its job is. It was written by firemen who don't want to see your house go up in smoke. The 30 amp circuit breaker on your dryer circuit is there to protect the wiring inside the wall to ensure it does not overheat and catch fire. Honestly, it is. That circuit breaker is not there to protect your appliances. It is there to protect the wiring and connectors. Connecting a 15 amp appliance to a 30 amp circuit "should" present no hazard. After all, how many of us plug in lamps wired with 18 guage wire (rated at about 6 amps) into a 20 amp standard wall outlet? You put a partial short in the lamp and the wire / plug will melt before the circuit breaker pops..