Actually, if you are trying to contrast neutrino oscillations to the paradigmatic $\bar K^0-K^0$ strangeness oscillations, they are both traceable to the W-boson interactions, so no new particles needed. (You only need new GUT intermediators for the highly speculative $\bar n -n$ oscillations.)
It is assumed you are familiar with the WP background on Neutral particle oscillations and Neutrino oscillation, as you assert.
In both cases, the respective particles are produced in a "flavor eigenstate",
that is a superposition of mass eigenstates dictated by how the weak charged vector boson (W) couples to fermion currents in a manner athwart different generations, thus violating a quantum number (e/μ/τ -ness; respectively, s which turns into u whence an $\bar s$ in a celebrated doubly weak box diagram,
. The non-diagonal mass matrix so engendered is then diagonalized, ready for propagation).
Once produced, the mass eigenstates propagate independently, and their phases have shifted when they are detected by a reverse weak process, also detecting "flavor eigenstates" (actually, mass eigenstates of the weak isodoublet partner fermions, perversely used to anchor/tag "flavor".)
In conclusion, neutrino oscillation is quite similar to strangeness oscillation; it is just that, in the former case the propagating states are ultralight fermions, and in the latter one relatively heavy bosons (pseudo scalar mesons), a billion times heavier. They all fit into the standard model quite well at present.
While novel, unexpected, interactions are conceivable for neutrinos, their oscillation by itself does not even hint at, let alone necessitate such!
Neutrino production and absorption interactions are purely weak, W induced, if that is what you are asking in part of your question. Deep inelastic scattering experiments starting in the 1970s have provided more detail on that aspect of neutrinos than any other one!