The Pokeathlon was an amazing feature to HG/SS, for me personally. It's probably one of my favourite additions to the game as it's unlike all the other additional mini-games in other generations and spinoffs. Usually I find myself rather disliking the mini-games in Pokemon other than the poffin baking and I thought this would be as boring, but how wrong I was to judge that!
Really it's a great way to take a break from continuous training and it's essentially competition in a whole new way. The events were fun to partake in, the contestants were rather good and the Supreme Cup was an interesting concept as you got to participate against famous people in the Pokemon world.
For the first time, I was hooked for hours in a Pokemon mini-game and not to mention, the prizes were fantastic as well. You could get items that weren't usually available till post-game early and that was great! The prizes were affordable as well only costing at most 5000 Pokeathlon points or even lower from memory. But yeah overall I loved the Pokeathlon and I hope it makes a return in future games!
I didn't really have a strategy honestly. But usually for each course, I would use Pokemon from my team that had the best stats overall in that course (e.g. Pokemon with the most stamina participates in the stamina course) But I found myself mainly using Crobat and Espeon throughout my playthrough.