Do solid-state amps take pedals well? No not really; digital solid-state amplifiers aren't very suitable for use with pedals. Although more reliable than their valve-powered counterparts, solid-state guitar amps can sound lacking and don't deliver that indescribable feel and response that you get from a tube amp.

Can you use an overdrive pedal on a solid-state amp?

Overdrive pedals can work on solid-state amps and tube amps equally well. I advise you to use it on the clean channel of the tube amp, although you can certainly plug this on the channel of your digital amp.

Can you plug pedals into any amp?

Nearly all guitar pedals can be used for any amplifier regardless if it's valve, modeling, or a hybrid amp. You can run guitar pedals through the primary input of the amp or individual pedals into the 'effects loop' (usually reverb, delays, modulation) depending on the effect and the player's preference.