required wattage of chip resistors in audio opamp circuit?
Well there is clearly less then 6V in play anywhere, so that is ~2mA into a 3K ohm load, giving 12mW, so 0402 is probably fine from that perspective. 
There is however something to be said for physically larger parts as they tend to have lower excess noise.

I note you are specifying 0.1% parts, for resistors, but that PC92 &amp; 93 are not so tightly specified (Good luck with that!)? This will hurt CMRR at high frequency.

Also R110 should be 100 ohms or so, to ensure stability when driving long cables.

In the headphone case R110 should be 20 ohms or so, but may dissipate some power if the cans are shorted, or the jack is only partly inserted, calculate this assuming a short to ground and full scale output, a 1206 or so is usually sufficient. 

I note the lack of an output coupling cap, usually a good idea, 100uF or so with a 10k bleeder across the socket, particularly for headphones, DC offset matters (But for cans the coupling cap should be much larger to support low impedance units). If you think a phantom power accident is possible then make this cap a 63V part and wire it positive terminal to the socket, with the ESD diode where PC148 is, that way the diode is behind the build out resistor which will limit the surge current.