Is it possible to provide a sharper picture, and maybe turn the pot to different angles and post a couple of pics?
I think the front plant is a Fittonia, the rear right looks like a syngonium and the tall one is hard to tell maybe a Croton maybe an Aglaeonema. I can't really tell what that is on the front left.
Not having a drainage hole makes it very difficult, at best the soil eventually sours at worse the plants' roots drown and rot.
It's a nice arrangement but you could do the same by individually repotting them, and placing the pots in a group, or by acquiring a larger pot (with proper drainage holes) and lifting the whole planting into that.
I'm sure you could use that lovely pot for something else - it would also be fine for holding other plant pots, provided they are raised up on stones so they sit clear of any accumulating water.
It's difficult to drill holes in ceramics without cracking the pot but it can be done - maybe your local hardware shop owner could do it or a good handyman neighbour/family member?