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The thing is, with this question you're asking for the fundamental units. These are units that we pick only because of simplicity's sake, but in reality they're completely arbitrary. Time is defined through the use of length, length defined by time, mass is defined through gravitational force (which is, by definition, based on mass). Kinda silly, but here are the most technical definitions:
Length: 1 meter = Distance traveled by light in 1/299,792,458 of a second.
Time: an observed phenomenon, by means of which human beings sense and record changes in the environment and in the universe.
1 second = the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Mass: the property of a body to have weight in a gravitational field.
Charge: the quantity of unbalanced electricity in a body (either positive or negative) and construed as an excess or deficiency of electrons.
I found the definition of charge pretty similarly from a bunch of sites (definitions in textbooks are often convoluted and without substance), but this definition is purely superficial -- it defines nothing about the "charge" we assign to particles more fundamental than the electron. :P I'm pretty sure quarks don't have excesses or deficiencies of electrons.