The range of weak interactions is of the order of 1/M_W~.02 fm.
The range of strong interactions between baryons is of the order of 1/m_pi~1 fm.
The range of strong interactions between quarks is due to gluon-gluon interactions,
leading to a confining potential with a range of about 1 fm.
I think the OP was asking how to determine these things experimentally, not how to predict them theoretically.
The answers to these questions are completely different depending on whether you're talking about the strong interaction between two nucleons and the strong interaction between two quarks. The latter interaction is usually modeled with an interaction that is of infinite range, and that gets *stronger* with distance.
A very simple way to put an upper limit on the range of the strong force between nucleons is from the liquid drop model. The liquid drop model contains a surface tension term, and the fact that the liquid drop model does a good job of fitting nuclear binding energies tells us that this surface tension term is physically accurate. This implies that the range of the strong force is small compared to the diameter of nuclei.
Re the question of how to put a lower limit on the range of the strong force, I'm not sure what it would even mean to hypothesize that the range of the strong force between two nucleons was less than about 1 fm, since nucleons themselves are fuzzy and about 1 fm in size.
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