I've never played Thermopylae, but for 4-player FFA Modern & RG, I've gotten to 1900 after playing for a few weeks (so, not amazing, but better than the starting 1500). Here's how I improved my game, after, of course, reading the official instructions and also clicking on a link in there that led me to a blog written by someone who is really good at 4-player variant chess:
1) Go to the "watch" tab and watch high-ranked players' games. I watched people 2400+ playing. You can click on their games and then hit the left arrow to rewind their game to the beginning.
2) After watching several high-ranked games, I chose one of the openings that I liked, which I noticed some high-ranked people used. This helped a LOT, once I had a solid opening to rely on.
3) BUT, before copying an opening, make sure you pay attention to where your queen & king are on the board. In different variants AND when you're different colors, your pieces begin in different spots.
4) For me, the pawns were confusing, at first. It was often hard to tell which ones could capture my pieces, because the orientation of all the pieces was the same, but each person can only capture in "their" appropriate direction. If you're good at paying attention to where each color is located on the board and therefore who can move where, then it might not be hard for you, but for me I changed the settings to "all pieces rotate to the center" (or something like that). This made it MUCH easier to tell which pawns could capture in which direction.
5) Practice, practice, practice! Just play a lot.
6) I also tried to make sure I played against people pretty close to my own rating, so I wasn't getting slaughtered without a chance to learn, so I would cap the top rating at maybe a couple hundred above my own. Once I reached a ranking of about 1700, I made the bottom limit around 1600. This was so I wouldn't get a bunch of brand new players (the ones with "?" after their rating). You might THINK it's easy to win against brand new players (and sometimes it is), but at times the new people are actually really good, but their rating is low because they just started on the site. Therefore, you lose points for playing against someone lower than you, even though they're actually better players (I'm not sure if you lose fewer points against a "?" person, but typically when you lose against someone lower-ranked, you lose a ton of points).
That's all I got. I'm certainly not a champion player, but that's how I was able to improve my game a bit. Good luck!!
Please give me tips and tricks thank you!