Hi, Kerry, and welcome to G.E.
The multi-word verbs you mention are phrasal verbs, formed by a verb and a separable adverbial particle. Notice that, if a pronoun is used, you will need to insert it in between:
- You have to check in the deliverables after closing out the effort -> You have to check them in after closing it out.
When a noun phrase is used, it can be placed between the verb and the adverbial particle (unless the noun phrase is too long), or at the end. Therefore, both of your options are grammatically correct:
- The deliverable must be approved prior to closing out the effort / closing the effort out. (BUT: The deliverable must be approved prior to closing out the effort assigned to you / the effort in which you have been involved -> the object is too long to be placed in between)
- The developer checks in/out the deliverable / checks the deliverable in/out.
Unlike "out" in "close out," which seems to mean "completely," "in" and "out" in "check in/out" have a directional meaning. If the place of origin or destination is mentioned, then the adverbial particle will obviously have to be placed at the end:
- The developer checks the deliverable into/out of the system.