I agree with that comment of English Student: "enter a room" does not require "into." That's a point about syntax. But I think that your question was not about the syntax of "enter," but about the word order in some comparable situation, with a verb that would take a preposition.
Your sentences sound strange to me. I think that the most natural order (without fronting) would be "He entered the office slowly." Next, for emphasis, "Slowly he entered the office."
Those would be possible with a verb like "walked," which would take a preposition in this context. In such a case there would be three expressions to order: (1) He walked (2) into the office (3) slowly.
I think the natural orders (without fronting) would include.
- He walked into the office slowly.
- He walked slowly into the office.
Next in terms of naturalness, I think, you could say:
- Slowly he walked into the office.
Remaining arrangements don't sound to me like native syntax:
- Into the office he walked slowly.
- Slowly into the office he walked.
- Into the office slowly he walked.
I think that if I read one of those last examples I would assume that the author was not a native speaker, or that he was trying to produce some sort of literary effect.