The axial asymmetry of the charge- and spin-density distributions in Pi states is Studied via second-rank traceless tensors P-ii (ii = xx, yy, zz), namely, quadrupole moments (Theta(ii)), electric field gradients (q(ii)), and magnetic dipolar (T-li) hyperfine coupling constants (hfcc's), In linear molecules, it holds that P-xx not equal P-vv not equal P-zz for Pi, but P-xx = P-yy not equal P-zz for Sigma, Delta, Phi,..., states. Thus, traceless P-u in Pi states have two independent parameters, P-parallel to = P-zz proportional to [r(m)(3 cos(2) theta -1] and delta P-perpendicular to = vertical bar P-xx - P-yy vertical bar proportional to [r(m) sin(2) theta], with m = 2(Theta(ii)) or -3(q(ii), T-ii). All linear states have P-parallel to not equal 0, but only Pi states exhibit delta P not equal 0, as shown by hfcc's like c = (3/2)T-zz and d = vertical bar T-xx - T-yy vertical bar, as well as q(c) = (-q(zz)) and vertical bar q(2)/2 vertical bar = vertical bar q(xx) - q(yy)vertical bar. Little is known about Theta(zz) and delta Theta(perpendicular to) = vertical bar Theta(xx) - Theta(yy)vertical bar in Pi states since most experimental values (gas-phase) are rotational averages, and several theoretical studies have reported Theta(zz) but assumed delta Theta(perpendicular to) = 0. The diatomics studied here have X-2 Pi(1/2)(pi(1)) ground states, like CH and NO, or are of type X-2 Pi(3/2)(pi(3)), like OH, CF, LiO, and FO. The A(3)Pi(1/2)(sigma pi(3)) state of NH is also included. Our P-parallel to and delta P-perpendicular to values-calculated at the experimental R-e's with the B3LYP/aug-cc-pVQZ method-reproduce well the available literature data. The properties of the CF and FO radicals are not well-known so that our {c, d} and {q(0), q(2)} values should help t'uture experimental studies of their hyperfine spectra. Excluding OH, the complete quadrupole sets {Theta(zz), delta Theta(1)} are new for all species discussed here. For comparison purposes, Theta(zz) of a low-lying Sigma state is also calculated for each X-2 Pi radical.