Depends what you mean by "output power". If you're referring to the total power absorbed by your coil+sample being heated, then you can measure I and V with your scope and calculate power as you described.
Yes, any phase skew between the two will affect the measured power. The higher the Q of the resonant system, the greater this effect will be. You should check this phase skew by testing with a known resistive load first.
It might be better measure I and V across the combined series resonant circuit, that way V and I should be roughly in phase (minimizing reactive power in the measurement). The downside is your measurement will also include losses in the capacitor.
If you are referring specifically to the power into the sample being heated, I don't believe there's a way to measure this directly. Would have to characterize the resistance of the coil, and use that to make a correction to the measurement described above.