Ultra luminous X-ray sources (ULXs) provide unique laboratories for studying accretion and radiation under extreme conditions, with luminosities exceeding the classical Eddington limit for stellar-mass compact objects. The discovery of pulsating ULXs has established that at least a fraction of these systems host strongly magnetized accreting neutron stars. Yet the physical origin of the ubiquitous high-energy spectral curvature around 10 keV in ULXs remains unclear. In this talk, I will present a physically motivated, angle-dependent synchrotron emission framework developed to explain the high-energy spectra of magnetized ULXs. Unlike the conventional angle-averaged treatment, the framework retains the intrinsic angular dependence of synchrotron emission, allowing the observed spectrum to probe the geometry, magnetic field, and energetics of the emitting plasma. I will discuss the theoretical foundations of the model and its application to broadband observations of pulsating and hyper luminous ULXs. I will also briefly discuss some recent results on polarized radiation from strongly magnetized compact objects, along with multi-wavelength studies of a gamma-ray binary candidate. I will conclude by outlining my broader research direction toward relativistic particle acceleration, gamma-ray emission, and very-high-energy astrophysics, with future prospects for connecting multi-wavelength observations to investigate radiation and particle acceleration in extreme astrophysical plasmas.