Well, there are a few ways to do this. One way is to make a macro that is the equivalent of “Move Relative” - just this:
! _Move _Pause 0
With an object preselected, you run the macro, type the distance and pull the object in the axis direction you want (Ortho on) and click to set.
The Gumball is even easier, just click the arrow in the axis direction desired, type a number and enter.
Otherwise a very simple script for moving in X might be:
import rhinoscriptsyntax as rs
objs=rs.GetObjects("Select objects to move",preselect=True)
if not objs: return
dist=rs.GetReal("Distance to move in X?")
if dist is None: return
This could be modified/adapted for the other axes by changing the direction vector and the definition name.