Nodal line semimetals (NLSMs) host distinctive topological properties and unconventional collective excitations. While plasmons in linear NLSMs are well studied, those of higher-order dispersive NLSMs remain poorly understood. We investigate plasmon modes in 3D quadratic and cubic NLSMs within the random phase approximation (RPA), valid for rₛ≪1 but breaking down in the small-doping cubic regime where the density of states diverges. Deriving the one-loop polarizability and evaluating its coefficients numerically from the full 3D Lindhard integral, we find distinct carrier-density scaling laws: quadratic NLSMs exhibit ωₚ∼ n^(1/2), while cubic NLSMs show ωₚ∼ n^(2/3) at large doping crossing over to ωₚ∼ n^(3/4) at small doping. The n^(3/4) law is not quantitatively reliable: the diverging density of states drives rₛ>1 already at n∼10¹⁸ cm⁻³, limiting the observable window to at most 10¹⁸≲ n≲10¹⁹ cm⁻³; below this, beyond-RPA correlations are essential. These scalings originate from the power-law density of states and intraband (Drude) response, and are analogous in phase-space power counting to bilayer and trilayer graphene, respectively. The long-wavelength intraband polarization dominates the plasmon frequency, while interband contributions are subleading (two to three orders of magnitude smaller for Ω≪μ). Both systems share a plasmon anisotropy Ωₚᶻ/Ωₚ^⊥→√2 in the thin-ring limit, a generic consequence of the torus Fermi-surface geometry. This √2 doublet, though observable by HREELS, cannot distinguish quadratic from cubic dispersion; the density scaling exponent is the true distinguishing signature. Our results provide a framework for the collective dynamics of higher-order dispersive NLSMs and suggest experimentally testable signatures accessible by HREELS.