Learn Russian: После работы тебе надо немного отдохнуть.

The word надо (need to) is a modal. When we use it with a perfective verb like отдохнуть, we are focusing on the result or completion of a single, specific action. You need to get some rest and be refreshed. If we used the imperfective отдыхать, it would focus on the ongoing process or a general habit (like "you need to rest regularly").

Why does the sentence use тебе instead of ты for "you"?

Words expressing need, like надо and нужно, require the person who needs something to be in the Dative case. So the nominative ты (you) becomes тебе (to you). Literally, the sentence is structured like "After work, to you it is necessary to rest a little."

Why is it работы and not just работа?

The preposition после (after) always requires the noun following it to be in the Genitive case. Since работа is a feminine noun ending in -а, its Genitive form ends in -ы, making it работы.

Could I change the word order and say отдохнуть немного instead?

Yes, Russian word order is very flexible, so that is grammatically correct. However, putting adverbs of degree like немного (a little) right before the verb they modify is the most natural and common way to phrase it.