BCC High Entropy Alloys (HEAs) consist of many elements distributed at random on the BCC lattice. The collective fluctuations in solute/dislocation interaction energies, even in dilute binary BCC alloys, lead to the spontaneous energy-lowering formation of a kinked/wavy structure for both screw and edge dislocations, respectively, over characteristic lengths ζc,screw and ζc,edge. Dislocation motion starting from the kinked/wavy structure is determined by the energetics at scale ζc. New general theories for both screw and edge motion in BCC alloys starting from this basic phenomenon are presented. The screw theory is sketched briefly, and shown to accurately predict strength versus composition and temperature in Nb-Mo and Nb-W binary alloys. As for BCC elements, the necessary inputs are difficult to establish, especially in more complex alloys. Key comparisons to simulations help demonstrate major features of the theory. More importantly, the edge theory shows that edge strengthening can be sufficient to compete with screw strengthening. Moreover, edges can control strengthening, especially at high temperatures, in some BCC HEAs. The edge theory, for which all inputs can be computed easily, explains (i) the exceptional retention of strength measured in MoNbTaW and MoNbTaVW at temperatures up to 1900K, and (ii) why the V-containing alloy is stronger. The edge theory can be reduced to a simplified analytic form that enables efficient computationally-guided design of new alloy compositions predicted to have high retained strengths and strength-to-weight ratios. Several new compositions are proposed. The combination of both screw and edge theories enables assessment of strengthening versus composition and temperature across the entire domain of Cr-Mo-Nb-Ta-V-W-Hf-Ti-Zr BCC HEAs.