What type of Resistors be used with Triac terminals? 1/4 or 1 watt
As soon as the opto-triac turns on it should trigger the power triac and the dissipation in the resistors should drop to about nothing. 1/4-W is fine. 

If the resistors are 'frying' it's a good indication that your power triac is connected incorrectly, missing entirely or faulty.