Regarding units in Espresso: you can input your quantities in whatever units you like. However, it is your responsibility that your units are consistent, i.e. that you express all quantities with the same physical dimension (length) in the same units - Espresso does not check it for you. It is generally recommended but not necessary to use a system of units where the characteristic sizes and energies of your system are on the order of unity.
Regarding particle size: its definition depends on your potential, i.e. on your model, not on Espresso. Size is a well-defined quantity for hard spheres. If you are using any soft potential, then particle size is partly arbitrary. In the case of LJ potential, the repulsion at distances below r=sigma rises steeply, i.e. the particles rarely appear closer to each other than sigma. The effective "size" of LJ particles increases with increasing sigma, but for a given sigma it also depends on pressure and other interactions. Since the effective size of a particle depends on its interaction potential, you have to come up with your own definition, based on the properties of your potential. You could deduce it e.g. from plotting g(r) of your system.