By first-principles calculations, we investigate the strain effects on the charge density wave states of monolayer and bilayer 1T-TaS2. The modified stability of the charge density wave in the monolayer is understood in terms of the strain dependent electron localization, which determines the distortion amplitude. On the other hand, in the bilayer the effect of strain on the interlayer interaction is also crucial. The rich phase diagram under strain opens new venues for applications of 1T-TaS2. We interpret the experimentally observed insulating state of bulk 1T-TaS2 as inherited from the monolayer by effective interlayer decoupling.