Using three-dimensional magnetohydrodynamic simulations accounting for ohmic dissipation, we investigate the long-term evolution of the infalling envelope for ∼ 100,000 yr after protostar formation. The primary control parameter is the initial misalignment angle θ₀ between the rotation axis and the magnetic field, varied from 0^∘ to 90^∘. In all misaligned models (θ₀ ≠ 0^∘), the pseudodisk (or infalling envelope) surrounding the circumstellar disk develops a highly distorted and complex morphology. Gas accretion from the envelope proceeds through discrete, channel-like flows, producing asymmetric streams rather than axisymmetric infall. Protostellar outflows are launched even in these complex environments, and inflow and outflow regions are strongly interwoven. Outflows transport angular momentum anisotropically, leading to time-dependent changes in disk orientation and outflow direction, which further enhance envelope asymmetry. We examine the relative orientation between gas flows and magnetic fields and find that, although statistical tendencies exist, accretion streams cannot be uniquely characterized as either parallel or perpendicular to the magnetic field, particularly in strongly misaligned cases. We also show that most infalling gas accretes at nearly the free-fall velocity, with only a minor fraction significantly slowed within the pseudodisk. Asymmetric accretion and stream-like structures persist beyond 10,000 au, demonstrating that large-scale asymmetry can arise intrinsically. Our results show that complex streams and asymmetric envelopes naturally emerge from magnetized core physics, even in the absence of initial turbulence or external gas accretion.