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There are so many subtle differences and I don't think one can summarise these differences in a set of simple rules. When referring to food in general, 食物 (edit: or 食品) can be used. Note that 食物 is a compound word, which literally means "something (物) to eat (食)". Examples: 食物安全 "food safety", 红十字会正为地震灾民分发食物 "Red Cross is now distributing food to the ...
上 here means about（相关）. Try to understand it like this: 那个是我工作相关的东西 If you omit 上, it'd be understand as the item used for work rather than about. 那个是我工作的东西 sounds a bit like 那个是我工作用的东西. Anyway, both are rarely spoken for native Mandarin speakers. You'd better provide more context.
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