Your messy power strip is not going to clean up tangled cables itself. You could use zip ties to tidy up cables, but it’s kind of semi-permanent — it would be a problem if you want to unhook a power plug. A cable management box is perhaps the best way to go.
The box is designed to contain a power strip and enough room to store rounds of cable nicely. It also has a few openings where cables can come up and connect to electronic devices. The overall look is plain and minimalistic, while four ventilation holes at the bottom ensure the electronic component inside won’t be overheated.