I have written the three sentences again with an explanation in bold of the "hold over" part:
In #1, the child is given a small amount of food to ensure that he is not hungry again before lunch.
In #2, the man needed transport. When he arrived he couldn't afford the bike he really wanted so he bought a "clunker" (a cheap, low-quality bike) which was good enough for him to use while he saved the money for the Mission Bicycle.
In #3, the husband had enough medication to last/take until he could reach a pharmacy and get some more. He kept a small amount of spare medication in his camping gear in case he started to run out.
I don't know about AmE, but in BrE I don't think we use this very often. I would have used "to tide him over/to keep him going" in all three.