It isn't uncommon for power tool cords to use undersize power cords. There are two determining factors when choosing a wire gauge for a cord: 1) voltage drop over a given length and 2) heat generated by that voltage drop, which must never exceed the insulation temperature rating (even on the hottest of days -- and given that most cords are rated at 60C (140F) to 105C (221F), that usually isn't the primary limiter).
Because tool cords tend to be short in length, the voltage drop over that limited length is generally within accepted limits for the tool (by which we usually mean the 'motor').
Now, if you were going to extend that power cord -- or plug it into an extension cord -- you would obviously want to use a larger 14ga or 12ga cord to ensure that the maximum voltage drop remains within accepted limits.
That all said, if you are running this 2HP motor on 120V AC (which I am assuming by the 15A to 20A quoted), then you clearly cannot be drawing 20A! If you were drawing 20A then you would most likely be tripping your breaker/fuse quite regularly -- even without the extra loads you quote. Generally, on a 120V circuit, the maximum that any single device should draw is 16A, and if you are using the more common 15A plug/receptacle, then that maximum is 15A. From this, you can likely infer that your motor is drawing no more than 15A.
To really find out how much your motor is drawing, however, you will need to use an ammeter (clip on, or with a plugin induction coil) to measure the actual power draw -- or for the average user a Kill-a-Watt plugin meter will provide all the info you wish for 120VAC circuits of 15A or less (note that volt-amps (120V --or actual measured voltagte-- multiplied by Amps) will give a truer estimate of peak load than amperage, which will represent the average load over the course of the AC waveform for any device with a less than 100% power factor).