A new method of obtaining the strange form factors of the nucleon is presented, in which forward-angle parity-violating e-->p elastic scattering data are combined with nup and nu;p elastic scattering data to extract all three strange form factors: electric, magnetic, and axial (G(s)(E), G(s)(M), and G(s)(A)). In this Letter, nup and nu;p data from the Brookhaven E734 experiment are combined with the Jefferson Laboratory HAPPEX e-->p data to obtain two distinct solutions for the strange form factors at Q(2)=0.5 GeV2. More generally, combining the neutrino elastic scattering data from E734 with the existing and upcoming e-->p data will yield the strange form factors of the nucleon for Q2 of 0.45-1.05 GeV2. Measurement of G(s)(A) is crucial to the determination of the strange quark contribution to the nucleon spin Deltas.