"Traditional" would be games that take after the Dragon Quest/Final Fantasy school of design, but it could be applied to the overall presentation or to the gameplay or to both. Like, to use Star Ocean again, it would be a traditional RPG in that it's not a strategy RPG or any other kind of sub-genre, but it doesn't have a traditional battle system. Rather, it has a real-time battle system.

"Strategy" and "tactical" are the same thing. People just use "tactical" to confuse people, haha. They generally take after the Fire Emblem/Shining Force school of design, with grid-based map movement and all that jazz. More about the gameplay than story compared to traditional RPGs.

"Action RPG" is a stupid term that gets thrown around for anything and everything, and often for games that really aren't RPGs because silly people call them such just because said games have elements that are also often associated with RPGs. Usually the term is applied to adventure games, like Zelda, Secret of Mana, Illusion of Gaia, Alundra, etc. etc.