An analysis has been carried out to discuss the nonlinear MHD, steady, two dimensional, laminar boundary layer flows with heat transfer characteristics of an incompressible, viscous, electrically conducting and radiating fluid with variable viscosity over a surface stretching with power-law velocity in the presence of a variable magnetic field and nonlinear radiation effects. The fluid is assumed to be a gray, emitting, absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. Then the resulting nonlinear ordinary differential equations are solved numerically using the Nachtsheim-Swigert iteration shooting technique for satisfaction of asymptotic boundary conditions by Runge-kutta fourth order method. The numerical results for velocity and temperature distribution are obtained for different values of viscosity measuring parameter, velocity exponent parameter, magnetic interaction parameter, surface temperature parameter, radiation parameter and Prandtl number. Values for skin friction coefficient and dimensionless rate of heat transfer are also obtained numerically for variation of physical parameters.