The two phase part of the above post isn't accurate. House power in the US is "split phase " though it is generally called "single phase".
The easiest way to visualize 1, 2 or 3 phase power, think of a 1 , 2 or 3 cylinder engine.
With obsolete two phase power, the second phase sine wave is offset by 90 * ( quarter of a wave ) . The circuit was generally fed with 4 wires and motors had 2 separate windings to consume the power.
https://en.wikipedia.org/wiki/Two-phase_electric_power
With single " split " phase house power, sine waves are 180 * offset ( half of a wave ) . These systems have 3 wires but only use 2 depending on if 110 or 220 voltage is needed. No matter the voltage, everything remains consuming single phase. Motors have one winding that is used for run. ( There is sometimes a start winding that drops out after the motor is turning but that is beyond the conversation here. )
https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiXzuCKivjUAhXGyj4KHanNCPwQjBwIBA&url=http%3A%2F%2Fwww.globalspec.com%2FImageRepository%2FLearnMore%2F20122%2F240120SinglePhaseWavefor mTransparente0e210f2a73b4e2aa95274447e1b5892.gif&psig=AFQjCNHtmjLOfLLyT6KVjHAbdiLmzvDx9g&ust=1499547921437169
With single phase house power, one can get 110 by selecting a hot and a neutral. To get the other "phase " of 110 you select the other hot and same neutral. To get 220 you select both hots.
Three phase power is used for generation and distribution to your neighborhood. It is also used directly by industry. With 3 phase power, the sine waves are offset by 120* ( third of a wave ). This is very efficient because the power transmission is smoother and motors less expensive / more reliable. Motors have 3 windings.
I don't know the current rate , but don't see an electrician charging more than a few hundred $ to install a 220 system if the wire / outlet can be fastened to the wall. For a short run materials would be sub $ 50 and take an hour.
Installing a 220 V outlet differs only slightly from a 110 v outlet. The actual wire is the same, the breaker needs to be a 2 pole ( we are using both hots ) and the third terminal is a safety ground not a part to pickup 110 V. If the device like a clothes dryer needs 110 to run the motor and 220 to run the heater, 4 wires must be used ( 2 hots , one neutral and a safety ground )
At higher voltages, a smaller wire diameter can be used Vs running the same load at a lower voltage. A three hp single phase motor running at 220 V will consume 13 amps , A 14 wire gauge extension will work though the thicker 12 gauge is better. ( for house wiring, 14 G is good to 15 amps and 12 G to 20 )
The oven socket will be rated for 50 amps so the plug won't work directly. You could make a jumper cord to a 220 V 15 A socket but in theory the cord should have it's own breaker. Breakers are rated for expected load and wire size. If a compressor that consumes 13 A locks up and the load goes higher, the breaker won't trip the the compressor will become a heater element.