An analytical formulation is presented to study uniform extension-torsion behavior of helical birods. The uniformity in extension and compression reduces the set of governing nonlinear differential equations of birod theory to a set of nonlinear algebraic equations for the relevant unknown variables of a birod. Upon normalizing the algebraic equations, we note that the birod's coupled extension-torsion behavior in its natural state can be tuned by changing the birod's constituent strand's intrinsic curvature and twist, Poisson's ratio and the birod's stiffness parameters corresponding to inter-strand separation and rotation. Analytical expressions of the birod's extensional stiffness, torsional stiffness, extension-torsion coupling stiffness, effective Poisson's ratio, overwinding/unwinding effect etc. in the birod's natural state are obtained. In particular, we show that depending on the parameters chosen, a torsionally relaxed birod can undergo non-intuitive slow overwinding followed by rapid unwinding during its stretching as observed during pulling of a torsionally relaxed DNA.