Max wattage on 120v outlet on 20A 80% breaker on 3 phase
No.  You don't multiply by the square root of 3 unless you're drawing all 3 phases in a delta configuration, and then, you multiply the pole-pole voltage (208) not the pole-neutral voltage (120). 

When dealing with a single phase of wye or split-phase, it's exactly what it says on the tin: 

120V x 20A x PF1.00 x 80%.  1920W.  

It's not "downgraded somehow", 3-phase wye service is simply three single-phase supplies that happen to be out of phase with each other 120 degrees.   Just as split-phase is two single-phase supplies that happen to be 180 deg out of phase with each other.