Helically poled magnetoelastic tubes enable programmable extension, torsion, and inflation under magnetic loading, making them attractive for soft robotic and tubular actuation systems. Building on our previous variational formulation, we derive explicit closed-form expressions for the effective axial, torsional, inflation, and magnetoelastic coupling stiffnesses in the thin-tube limit. A consistent asymptotic reduction transforms the three-dimensional nonlinear magnetoelastic problem into a compact Cosserat-type model with analytically identifiable moduli that depend explicitly on the poling angle, elastic anisotropy, and magnetoelastic parameters. Unlike classical piezomagnetic formulations, the present approach captures geometry-induced coupling arising from helical magnetization and establishes a direct link between three-dimensional field equations and reduced-order structural behavior. The resulting expressions clarify how helicity governs chiral and non-chiral actuation pathways: azimuthal magnetic fields activate extension and inflation only in the presence of helicity, whereas axial magnetic loading induces deformation even for purely axial poling, with the torsional response depending on field orientation. The formulation recovers known limiting cases and yields physically consistent predictions across a range of material and geometric parameters. Order-of-magnitude estimates based on experimentally reported properties of magnetoactive elastomers further indicate that the predicted responses lie within realistic deformation regimes. The closed-form stiffness relations provide a rigorous and computationally efficient framework for rapid parametric analysis and support the systematic design of magnetically actuated soft tubular devices.