OK, most of these phrases (the English ones) carry some connotations with them, so here goes:
"Blast!" - very posh (stereotypical WW1 pilot/cavalry person ["Jolly good show, what?" etc.])
"Aw, shucks!" - American I'd say, I also associate it with children
"Good Heavens!"/"Good God!"/"Dear Lord!" - all also quite poncey (please note, however, that "Oh God" is fine)
"Blooming" - I'd avoid; can get away with it for "Bloomin' 'eck!" (similarly, "Flippin' 'eck/'ell!") if you have a cockney accent; can be used, but, as I say, try not to. "Blooming marvellous/fantastic!" is another very posh, toffy* expression. Note, "flipping" more acceptable than "blooming" but still too soft, try to avoid and avoid saying "flip" on its own instead of f*** AT ALL COSTS, unless you're under 10.
"Crikey!" - I wouldn't use, it carries two images for me: again, the stereotypical toff, but also associated with Australians. Of course, these are all stereotypes, but I'm just trying to get to the point.
Substitutes for shit:
"Sugar" - fine, go ahead
"Shoot" - bit stranger, I'd use "sugar" instead, but can be used
"Sheizer"/any others - I wouldn't
*toffy as in "spoken by/associated with a toff", nothing to do with the sweet