How to interpret different socket tester results with and without power strip?
Some of the sockets in your house and also your portable power strip have line/neutral reversal problems in the wiring.  Switching the wires twice switches them back.  You might want to get an electrician to check all of your wiring, or if you're willing to do enough research and it's legal in your area, fix it yourself.  You can't just go around matching same color wires though so if it turns out the problem is more complicated than just the plugs being connected wrong, it would be wise to hire a professional.
Line/Neutral reversal is a sadly common problem.  It can go unnoticed almost indefinitely, but it's better to correct and may be a sign of other bad practices.  Most device power switches switch the line wire, and if line and neutral are reversed, parts of a device could be unexpectedly energized even if the load is turned off and shock someone.  This is also a reason best practice is to have switches consistently on the line side.