"Crud" usually means "dregs" or "caked-on dirt". It's not really vulgar or offensive, as far as I understand. "Shit" is a strangely flexible word (as some swear words tend to be), so it can be literal or figurative. Perhaps the softer version you were thinking of is "crap" (also rather flexible). Swearing isn't off-limits to the well-educated! ;) If anything, some of the swearwords can be beautifully creative. Perhaps you want phrases which express the emotion without directly swearing? You might hear "Sugar!!" yelled out, in frustration or shock.

i dont't know

This is more of a US thing, but my UK understanding is they technically mean the same, but 'crud' is considered less offensive. Shit is also often used as a substitute for other words; 'I'm not taking your shit'...which has nothing to do with actual shit.