Firstly, the Panasonic LX7 is in a totally different class to the other 2. The Panasonic LX7 will give you much higher quality photos and much, much, much better low light photos but a much smaller zoom.
If you are mostly going to be shooting close-up sorts of subjects, then the Panasonic LX7 is definitely the one to go for.
Secondly, the Olympus SZ31mr is not a great camera. People get wowed by it's big zoom, and think that because it gets closer that it is better. It isn't. That's not to say that it's a bad camera, it isn't, just that there are others that are better.
IN regards to the Panasonic TZ30. It's okay. Quality wise it's about the same as the Olympus SZ31. But it's a bit smaller, with a slightly smaller zoom (20 VS 24), but with the addition of a few nice features (GPS, Touch Screen).
In this category, I would probably ignore both the Olympus SZ31 and the Panasonic TZ30 and I would get the Canon sx260hs. This camera has the same 20x zoom range as the Panasonic, with the same full manual and full auto controls, GPS, etc. But it's low light performance is better. Further, compared to the Olympus or Panasonic, you also get cleaner images at ISO 100/lower ISOs, etc.
Also, the Canon or Panasonic will give you actual manual control over your shots, which the Olympus doesn't have from memory.