You like RPGs and occassional strategy games, so Fire Emblem sounds like a must. I've heard Luigi's Mansion compared to the point-and-click adventure genre, so I recommend looking into that one. Ace Attorney and Professor Layton are more typical point-and-click type games.
If you're a righty I suggest trying out Kid Icarus: Uprising. If you're a lefty, I'm sorry.
Oh yeah and Pokemon.