To be honest, I really know nothing about the type of gameplay in Advance Wars. However, from this video I saw (I think its yours,
http://www.youtube.com/watch?v=HEFG6Zv_ges&feature=channel&list=UL) it seems to be a turn based strategy game. (correct me if I'm wrong).
Something like that would be pretty complicated to get to work with RMX-OS in my opinion, but here's how I would start going about that. First of all, you will need some way of setting up matches between 2 players. I'd recommend having each map represent a different match. For that to work, you would theoretically have to have a number of different maps for matches equal to half the number of total players that can be online at once. (Since each match would take 2 players). Now to keep track of which maps are being used and which ones are empty, you could have a server extension which keeps track of an array of available maps. Whenever a match starts on one of the maps, have the client send a message to the server to remove that map from the list of available maps. Similarly, you could have the server keep track of an array with the ids of players looking to start a match. When another player tries to join a match, the server could randomly choose a player from the array of player's already looking for a match and pair them together. The server could then remove the player from the array, send a message to both clients transporting them to the next vacant map, and setup the match itself. Alternately, you could create a nice looking scene where players can actually choose their opponents instead of it being random.
Now on for the match itself. First of all, the match will need to have 1 active player and one inactive player (assuming its turn based). When the match is started, the server can select one of them to be the active and send a message to the client changing some sort of variable to true. The other player would have that variable set to false. When it is a players turn and they make a move, have the client send a message to the server with the move they made. The server could then send that message back to both clients so that the move is actually done. When a player ends their turn, the client could send a message to the server having the "active" variable switch to true on the other player, while switching it to false on the currently active one.
As I was writing this, I thought about how the server would know who the opponent was so that these variable changes get sent to the right person. Theoretically, anything being sent to both players could simply be sent as a "map message", sent to all clients on the map. However, otherwise it would have to be sent to 1 specific person. I haven't tested it, but to get the other player on the map, you could use this in the server extension when receiving a message from the client.
client.sender.get_map_clients
That would be in the client update section of the extension.
Oh, and if you want to make it online compatible as well as offline... I honestly don't know what I'd do about that. I suppose you could have it only load the RMX-OS stuff if its on multiplayer mode. An alternate (possibly easier) way would be to make an entirely separate game for the multiplayer mode, and then launch it through the main game with something similar to Blizzard's multi-game launcher (
http://forum.chaos-project.com/index.php?topic=119.0)
Anyway, that's just a quick idea of how I'd do it with as little planning as possible. If you want some clarifications, actual code examples, etc just let me know. If you have a better way, also let me know. I'm sure Blizzard or someone is looking at what I wrote and thinking how much easier/better it could be.