  The behavior of two-dimensional Ising spin glasses at the multicritical point
on triangular and honeycomb lattices is investigated, with the help of
finite-size scaling and conformal-invariance concepts. We use transfer-matrix
methods on long strips to calculate domain-wall energies, uniform
susceptibilities, and spin-spin correlation functions. Accurate estimates are
provided for the location of the multicritical point on both lattices, which
lend strong support to a conjecture recently advanced by Takeda, Sasamoto, and
Nishimori. Correlation functions are shown to obey rather strict
conformal-invariance requirements, once suitable adaptations are made to
account for geometric aspects of the transfer-matrix description of triangular
and honeycomb lattices. The universality class of critical behavior upon
crossing the ferro-paramagnetic phase boundary is probed, with the following
estimates for the associated critical indices: $\nu=1.49(2)$, $\gamma=2.71(4)$,
$\eta_1= 0.183(3)$, distinctly different from the percolation values.
