if the power strip is a decent design (and complies with the electrical safety rules for nearly every country in the world) you have your PSU grounded by pluggin it into that strip. If in doubt - plug it directly into the wall outlet.
If you are working in a carpeted room you definitely want to remain grounded all the time, preventing any static charge from building up. The easiest would be to get an antistatic wrist lead to keep yourself grounded through that. But you can improvise that by wrapping a highly flexible stripped copper cable around your wrist and securely connecting it to the outside (!!!) of the PSU casing while the PSU is still plugged into the wall. Before you do that take a line tester and make 100% sure the grounding/earthing in your building is ok. I'm in Kenya and boy - I could tell you stories how electrical installation can be messed up, sometimes ending up with half of the mains voltage on your ground contact. You don't want to expose yourself to a nice 60 to 120 Volts wake-up call, do you? Maximum A/C voltage considered safe on *intact* skin (no open wound) is 42 Volts. Anything above may be lethal. So please take care.