1) Use "move in" when you're talking about moving into a building [a building that you intend to use regularly, like an office]. Eg. "We are moving into our new house on Friday" = "We will move to and start living in our new house on Friday". OR: "Our company will move in to our new London office next week". OR: [Imagine that you are already inside the building you are going to move into]. "We will move in here in a month's time" = "In a month's time we will move to this location and start using the building [or living there, if it's a house]. --- 2) "Move on" means to "move past", "move beyond" and "stop caring/thinking/being preoccupied about something". For instance, one can "move on" after a relationship breaks down. "I split up with my girlfriend two months ago. I've been really sad but I think it's time to move on." = "I've been so sad since I split up with my girlfriend two months ago but I think it's time now to stop thinking about / being preoccupied with her." "It's time to move on from our relationship with X Company." = "It's time to move past / stop dealing with with X company" --. 3) "Move out" is the opposite of "move in". So it means leaving your home or a building that you use regularly [like an office / factory]. "I'll be moving out of the house next Friday" = "I'll be leaving the house next Friday and moving elsewhere". "We'll be moving out of our office in New York next Friday and, in a month's time, we'll move into our new office in Los Angeles" = "We'll be leaving our New York office next Friday and will be moving into our new office in LA". -- As a final note, use "move into" as I have described in (1) above. You can use "move to" more widely to simply mean moving location temporarily but I'm sure you're already aware of that. -- Ingat ka lagi :)!

"Move on" and "Move forward" are both pretty similar. You can use them pretty much interchangeably but you'd usually use "move on" when you were talking about human relationships. "Move forward" would usually be used more with politics/business. "Moving forwards" is more like "moving onwards" though and doesn't necessarily imply a strong sense of "moving on" / "departing" from an old relationship. Things like: "We are moving forward with our plans to double our sales by the end of next year" are good. You would say: "We are moving onwards with our plans to double our sales by the end of next year" as opposed to using "moving on". Sorry I can't give much more explanation in the comments section because I can't format here so it'll just be a big mix of text ^_^. Ingat ka :)