  We propose a general framework for constructing a large set of nodal-point
semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically
($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify
a new perturbative route to access various strongly interacting non-Dirac
semimetals with $d_Q>0$. As a demonstrative example, we relate a two
dimensional anisotropic semimetal with $d_L=d_Q=1$, describing the topological
transition between a Dirac semimetal and a normal insulator, and its three
dimensional counterparts with $d_L=1$, $d_Q=2$. We address the quantum critical
phenomena and emergence of non-Fermi liquid states with unusual dynamical
structures within the framework of an $\epsilon$ expansion, where
$\epsilon=2-d_Q$, when these systems reside at the brink of charge- or
spin-density-wave orderings, or an $s$-wave pairing. Our results can be germane
to two-dimensional uniaxially strained optical honeymcomb lattice,
$\alpha$-(BEDT-TTF)$_2\text{I}_3$.
