The PCE can use all sorts of 'resolutions', but it's misleading. For example, 320 mode(horizontal) has the same pixel dot size as 336, 344, and 352. A more correct way is stating the dot clock. PCE has 5.37mhz, 7.16mhz, 10.74mhz which usually corresponds to 256xYYY, 336/344xYYY, and 512xYYY. The PCE can have from 1 to 512 scanlines vertically, but it can only show a max of 242 scanlines (any higher setting is not shown). It also doesn't effect the "dot" size of the pixel when you set the number of displayable scanlines, less than 242 and the image gets "letterboxed" so to speak.
As far as which games? Rtype, Forgotten Worlds... I don't remember what else, use the 7.16mhz dot size. Most games use the 5.37mhz dot size because it has a better ratio for sprites per scanline. For 10.74mhz dot clock, one DMA design game uses it for the logo at startup and TV Sports basketball uses it in parts. Coryoon has a mode where you can see 4 screens at once, that uses the 10.74mhz mode.