Generally speaking, these three words express different meanings according to situational applications and different contexts. I suggest that you can use it according to different situations.

Review: Review reading. For example, review the plans made and review the reports sent by various groups. The appropriate occasion is the need for leaders to guide the designated plan and report, and please have a look at it.

Take a look: browse, for example, the resume for job hunting, and read my own humble opinion. Appropriate occasions are things that need to be checked by superiors, things that subordinates say to superiors, and honorifics.

Check: Check and accept it. For example, please check your courier, please check your documents and sign. It is generally used at the end of email files between superiors and subordinates, which can be polite and meticulous.