@Tes yeux noirs,
Some power strips have surge protectors built in. Some don't.
Some people think that all power strips are "surge protectors". They aren't.
In view of this, it may be worth asking the OP if the power strip does or not have a surge protector built in. If it doesn't, we have all been barking up the wrong tree.
The answer remains the same, that you generally can use the on/off switch on a power strip to control all of the things connected to the strip, and a bunch of LEDs are unlikely to cause trouble, but if you connected a number of heavy duty appliances and tried to switch them all at once, you could find the switch burning out after a number of on/off operations. Do not exceed the rating of the power strip. Listen for a fizzing or frying sound at the moment of operating the switch.