We know that there are no true synonyms in the Torah. What does each of these connote? (to pass the test here - i googled and did not find anything)
"Cherem" implies that it is "off limits" from the general population; it will belong either to the kohanim, the Temple, Hashem, sacrificed, burned, something like that -- the Average Joe isn't going to get anything out of it.
As for the other two, check out Rashi, Bamidbar 31:11
שלל. הֵן מִטַּלְטְלִין שֶׁל מַלְבּוּשׁ וְתַכְשִׁיטִין: בז. הוּא בִזַּת מִטַּלְטְלִין שֶׁאֵינָם תַּכְשִׁיט:
Shalal is clothing/jewelry; baz is any other (non-human, non-animal) object.