  We consider the possibility that sterile neutrinos exist and admit a
description as unparticles; we call these {\em unsterile} neutrinos. We then
examine the nature of neutrino oscillations in a model where an unsterile can
mix with two active flavors with a very simple mass matrix of the see-saw type.
Despite these simplifications, we find a number of remarkable features, all of
which will occur generically when more realistic cases are considered. These
include momentum dependent mixing angles, "invisible" decay widths for the
unsterile-like mode, as well as the inheritance of a non-vanishing spectral
density for the massive active-like modes. We also obtain the disappearance and
appearance probabilities for the active-like neutrinos and find remarkable
interference effects between the active and unsterile neutrinos as a
consequence of threshold effects, yielding new oscillatory contributions with
different oscillation lengths. These effects are only measurable on short
baseline experiments because there both probabilities are suppressed as
compared to mixing with a canonical sterile neutrino, thereby providing a
diagnostics tool to discriminate unsterile from canonical sterile neutrinos. We
conclude with a discussion of whether these new phenomena could aid in the
reconciliation of the LSND and MiniBooNE results.
