I've had success using dining chair & table combos on quarter tiles, but I found I have to be exact in placing them where they need to be slotted for the objects to function. I start with placing them snapped to a full tile, and then activating the cheat and carefully moving each object the same distance in quarter tiles. In occupied lots, I check by going to Live mode to make sure the chairs push in to the table and sims can eat a meal.
I wouldn't say that I've tried every chair and table in the catalog, but the ones I've tried have worked (including your slaved dining tables, HugeLunatic
). I haven't experimented as much with desks, but I *think* I have had success with them as well.
I have no idea about diagonals, though... I rarely use the 45-degree cheat except for decorative objects and the occasional living chair.