Does a really strong immune system prevent a stomach virus or bacterial infection such as salmonella, e. coli, etc...?

It depends: Salmonella and e coli can devastate even the strongest individual. Symptoms from these infections depend on the how strong the exposure is to these organisms and the over all health of the patient. If the exposure is small enough then it is possible that no symptoms will occur. If the exposure is still small but the recipient is already weakened from something else then problems may occur.