  We consider a spinless $t$-$t'$ ionic Hubbard chain at 1/2 filling and large
hopping ratio $t'/t$. In this limit the model adequately maps onto a weakly
coupled triangular ladder with a potential interchain bias. The low-energy
properties of the system are formed due to the interplay of geometrical
frustration, correlations and charge imbalance. We derive the effective
field-theoretical model to study universal properties of the model in the
scaling limit. We show that at full dynamical frustration the ground state of
the ladder represents a repulsive version of the Luther-Emery liquid with
dominant orbital antiferromagnetic correlations exhibiting the slowest
power-law decay in the ground state. Pairing correlations also display
algebraic order but are subdominant. At an incomplete dynamical frustration a
finite commensurability gap is dynamically generated, and the fluctuating OAF
transforms to a long-range ordered state with a spontaneously broken time
reversal symmetry. The mass gap in the spectrum of relative density
fluctuations gets suppressed upon increasing the potential bias.
