I’m not an electrician but I’m going to assume that if it’s weather protected enough that you’re willing to leave a stereo and a projector out there a power strip would be no big deal.
If it was up to me I would have an electrician install 4 outlets with locking covers on the corner of the house where I will be but that is not an option.
My local hardware store has these outdoor outlet covers that are basically a large plastic cover where the power cord comes out underneath. If you are going to put your stuff in a cabinet (“plastic box”), just put your power strip inside the cabinet as well.
That’s my suggestion as well. Take it a step further and unplug it from the wall when you’re not using it, especially if it’s going to be more than a few days. Also, if this is a permanent fixture, find away to seal the hole shut where the cord passes through the box or you’ll end up with mice living in the box.
Finally, before you start the project, fix the water spigot that sprays water on the outlet. Do that first. That’s just asking for problems. Even if you have a GFI outlet, you’re still going to end up with corrosion.