What laws (formulas) govern the fundamental forces of nature?
None.
Columb's law and Newton's law of gravitation classical explanations of electrostatics and gravitation,respectively.
But the are no analogus formulas for fundamental interactions. They must be described in the context of Quantum field theory.
QFT is to complex to give you a formula where you can plug in some numers. For example, to study a simple interaction you will need to calculate many Feynman diagrams (integrals).
The EM, for instances is described by the Lagrangian: $\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+j^{\mu}A_{\mu}$
See: What is the Standard Model equation which unified Strong, Weak, and Electromagnetism?What is the Standard Model equation which unified Strong, Weak, and Electromagnetism?