Samanjoonii's answer is right - you use 'whom' for the object of the sentence. 'Whom' is an object pronoun like me, him, us and them. So - Whom did she want a job with? - Whom did she wait for? are both correct sentences. But - and this is a big 'but' - it's also worth pointing out that both these sentences sound extremely unnatural to native speakers. They would earn you top marks in a formal grammar test, but the fact is that we don't use 'whom' in this way. A native speaker would never naturally say 'whom' in these particular sentences. These are simple everyday questions, and 'whom' is not used in sentences of this type in modern English. In this sense, the 'correct' versions are: Who did she want a job with? Who did she wait for?

Following on from Tony's point about not putting a preposition at the end of the sentence, it's worth mentioning that there are three possible versions: 1. With whom did she want a job? For whom did she wait? This is ultra-correct, but rarely used. It sounds unnatural and over-formal, especially for a simple everyday question like this. 2. Who did she want a job with? Who did she wait for? This is completely natural. This is what all native speakers would say. 3. Whom did she want a job with? Whom did she wait for? This is very unnatural indeed, partly because it's a mixture of formal and informal. I doubt whether any native speaker would ever say this.

In more traditional/formal English there is a convention that a conjunction should not appear at the end of a sentence. (The humorous version of this is 'A conjunction is something you should never end a sentence WITH.) Once this is understood you can move on to your first sentence. If we re-write this to follow the convention it becomes With who did she want a job? We can now apply a second convention that after a conjunction 'whom' is used. Your sentence now becomes 'With whom did she want a job?' This is grammatically and stylistically correct but does sound formal to the modern listener. As you have now established 'whom' is the correct form you can go back to your original construction and say 'Whom did she want a job with?' The second pair of examples are incomplete sentences. I assume the missing word is 'for' If this is the case you can now apply this method and see the outcome for yourself.

Here are the answers to your question: - Whom did she want a job with? - Whom did she wait for? ---- Rule: Use "whom" when you could replace it with "him". Rule: Use "who" when you could replace it with "he". Source and Further Reading: Who vs. Whom- http://data.grammarbook.com/blog/whowhomwhoeverwhomever/3/