I assume that we are are talking about different domains?
If this is the case I completely agree with Scott. Make a list of user, export them all as an csv. Then go through the CSV making sure to assign them to the relevant groups and give them the relevant permissions. The go ahead and create them in the company domain.
I assume that your company domain has some sort of home folder policy? It auto creates the user's home folder on the file server you want to keep in place? If so, then just let it do this as you manually copy the users over. Then simply copy the user's data you want from their old home folders onto the new server with something like Robocopy, but force a permission inheritance when you do so (this way they'll actually be able to access their stuff).
All of that, the exact process would really depend on the number of users you are talking about, sub 200 I'd go this route, but phase it in my department or something like that. Sub 50, do it all at once over a weekend. More than 200 may require a completely different approach.
Permissions on their old file server are going to be a problem, but if you are doing all the copying over a weekend rather than phased in, just use the admin account to grab ownership of the files and open up full permission to that admin account. Then when you copy then over the inherit permissions should then allow only them to access the files (or them and the admin account). I doubt the ownership would be an issue, but if it is there is more than likely a power shell script you can run to replace the ownership of the files to that of the containing folder (ie the user's home folder).