  We prove ergodicity in a class of skew-product extensions of interval
exchange transformations given by cocycles with logarithmic singularities.
This, in particular, gives explicit examples of ergodic $\mathbb{R}$-extensions
of minimal locally Hamiltonian flows with non-degenerate saddles in genus two.
More generally, given any symmetric irreducible permutation, we show that for
almost every choice of lengths vector, the skew-product built over the IET with
the given permutation and lengths vector given by a cocycle, with symmetric,
logarithmic singularities, which is \emph{odd} when restricted to each
continuity subinterval is ergodic.
