This is in a country where power outlets have individual switches. The situation:
[ul]
[li]Plugged in, switch on: light on[/li][li]Plugged in, switch off: light glows faintly[/li][li]Unplugged: light off[/li][/ul]
Why is it glowing? Is there a wiring problem in my house? Hmm maybe I should try the power strip on another outlet.
Many power strips use a neon lamp to indicate power. These have a huge impedance, and will illuminate at even the smell of nearby power. I would assume the lamp is hung across the active and neutral lines in the power strip. In principle, if the power outlet is turned off there should not be any power, not even enough around to illuminate a neon globe. However, if the power point is miswired, with the active and neutral reversed, and thus the neutral is cut, but the active remains when the outlet is turned off, there could be enough capacitive coupling in the lead to the ground wire of the strip, that the lamp does illuminate a little. So, I would be worried enough that I would have the outlet checked for a miswire. Especially if the strip does not behave the same on other outlets.
I would get a tester first, useful to test all your outlets, and useful to own. Much cheaper than getting some out out needlessly, if it is OK. (Arguably wasted money if you do need to get someone out to fix the problem. But if you test all your outlets you will know the scope of the problem ahead of time, and a tester is something good to have on hand.)
Will those simple testers tell you whether an outlet on a switch is having its neutral or its hot switched when the switch is off?
Do you have a voltmeter, or know someone you can borrow one from? You could test the voltage between all three outlet slots with the switch on and with it off. If there’s a current draw on that circuit from some other outlet, the neutral might not be a 0 volts relative to ground.
The switch on the outlet… is it one of those “illuminating” type (i.e. has a built in light that illuminates when the switch is off)? If so, then that explains it. If not, then I suspect the switch has excessive leakage resistance when it is off.