Hi! Okay so in American English should is not really used often as the beginning of the sentence, but some people do, but regardless people will understand you.
If you need help, then you should ask.
In your examples without should, the first one "If Tom phones while I'm out, tell him I'll call him back later." This one is correct, but is a little more slangy. I would use this sentence more than the example sentence. "If Tom should phone while I’m out, tell him I’ll call him back later." But should is not entirely necessary for the next two sentences, but it changes the ending of some of the words without the word.
We have no jobs at present. But if the situation changes, we’ll let you know.
If Tom phones, tell him I’ll call him back later.
Again, this is very slangy and informal so I would use the should's if you were speaking to someone you did not know.