I only trade if it will gain me 10 or 12 troops, but only using Artillery if I badly need the troops. Otherwise just when I have a set of different cards. However if I get a 4th card the same, I will trade.
As for strategies, Australia is always a good shout if you can get in there. Otherwise just slowly build up an army somewhere (anywhere), taking 1 territory at a time, so as to not provoke anyone into attacking you (and thereby attacking other players) until you have enough to split up the army and take (and crucially HOLD) that continent.
Also, be willing to ADAPT to changing circumstances. Move continent if you have to! Don't commit suicide or martyr troops by attacking a player when you don't have enough to continue to hold your territory. If someone looks as though they're about to attack you, move your troops out of harm's way and just let them take the 1 instead of 25.
Referring to Fixed Bonus, not progressive, in my first point.
Another tip: ally with everyone right at the start of the game! :)