Josh continued to use his trusty Ovation GP guitar as his main ax, but can also be seen playing a Telecaster, an Epiphone Dot, a Gibson Marauder, and Gibson ES-225 among others. Of course, most of the times they are still tuned down at least a full step, but a C-standard tuning is not rare. QotSA is using various kinds of amps, but the most recognizable ones are the Ampeg Vt-22 combos and Ampeg VT-40's with 2x12 cabs, the Ampeg V, and the Vox AC30.
As you can see from the picture Homme is using a huge arsenal of pedals while playing; some of them might be just there to mislead people, he is famous for trying to hide the secret to his sound. Although he does a good job at masking his stuff, we'll try to pinpoint the cornerstones of his heavy sound. The two main overdrive/distortion pedals he uses are the Boss SD-1 and the Fulltone Ultimate Octave, the latter is a fuzz and an octave pedal in one. He also uses EHX POG Octave Generators and you can also see a Boss octaver on the picture. He uses multiple volume and wah pedals; you can't go wrong with a simple Dunlop CryBaby. Also, you can see some phasers on the board, an MXR Phase 90 and an EHX Small Stone. Since his rig is quite huge, if you want to dig deeper, you can look up the complete list at http://www.uberproaudio.com/who-plays-what/217-queens-of-the-stone-age-josh-homme-guitar-gear-rig-and-equipment.