What is the difference between 整理 and 整頓 ?Feel free to just provide example sentences.

1) The meanings of both words are almost same: Clean up. There're little diffrences and I think the explanations PigPanda writes are right.

2) Grammatically, 整頓 is possible to use as one word, but we don’t use it and it’s unnatural to use without using with 整理.

3) When using “整理整頓“, it means “Tiding up” and literally the emphasized version of 整理.

整理: clean up
整理整頓: Tide up


Voca Ex.)
Correct: 整理整頓 (整理 always comes first.)

Incorrect: 整頓整理


Sentence Ex.)
Correct:
(私の)引出しの中を整理しなきゃ.
I should clean up my drawers.

Correct:
整理整頓は大事だよね
Tiding up is important.

Incorrect:
(あなたの)服を整頓した方が良いよ。
You had better to 整頓 your clothes.