What are the differences between 金、料、代、and 費？

Question

For example, 入学金 is correct; we can't use 入学費・代・料; that's not 日本語.

But all of them mean costs for something. Could someone please explain this?

Answer 1

The top few pages of Google search result already contain lots of fruitful answers, only if you can read them:

「…代」と「…料」はどう使い分けますか？ (Japanese)
中上級を教える人のための日本語文法ハンドブック (Japanese)
JeckGroup (Vietnamese)

The following is basically a summary of them in English, plus what little I know.

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～金:
A general term for money in specific situations, not necessarily in exchange for something, might even not cost. It's a fallback option when none of the rest could apply.

保証金, 入学金, お祝い金, 所持金, 補助金, 契約金, 敷金, 賠償金

～料:
Charge or fee for activities done, typically charged by organizations with a predetermined amount of money.

授業料, 手数料, 送料, 使用料, サービス料, 通行料, キャンセル料

～代:
Price or charge in exchange for concrete (doesn't mean tangible) items. Most widely used.

食事代, 飲み代, タバコ代, バス代, バイト代, 電気代, 地代, 修理代

～費:
Overall expenses for specific activities, not used for detailed items.

医療費, 交通費, 学費, 生活費, 食費, 参加費

BONUS

～賃:
Fare or transportation fees, otherwise limited to a small number of idiomatic expressions.

運賃, 電車賃, 家賃, 工賃, 手間賃

～料金:
Similar to 代 or 料, just preferred in charges for constant everyday services.

通話料金, 電気料金, 高速料金, 基本料金

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So, your 入学金 is a good example of unspecified expenditure. Not only you in Japan wonder why and for what they have to pay it.