Originally Posted by hausarzt

Thank you for the suggestions folks.
Better late then never, here is a quick update:

After trying many things (removing plugins, caching on/off....) suddenly my site went back to normal.
Since 4 days, it's under high load again. No changes where made. Logs show nothing suspicious.

Time to change the host I guess. I am moving to a VPS soon.
Hopefully this will fix the site performance.