I think the simplest way is to test the solution made with the electrolyte for conductivity of electricity.
If you can access a conductivity tester (two wire leads connected to a small light bulb and a battery will do), make a solution with the electrolyte and test how well it conducts electricity.
A strong electrolyte will conduct very well, and the bulb will be bright. A weak electrolyte, not forming many ions when dissolved, will cause the bulb to glow only dimly, if it glows at all.
"Strong" in this sense means forming ions in a complete reaction:
#AB rarr A^+ + B^-
If this reaction is complete, (meaning all the solid that dissolves changes to ions), the electrolyte is strong. NaCl is and example.
If it is possible for the electrolyte to dissolve, but not form ions to a large extent, it is weak. Acetic acid is an example
Only about 1% of the acid forms ions when you dissolve it in water.