  We discuss the definition and the energy evolution of scattering amplitudes
with $C$-odd ("odderon") quantum numbers within the effective theory for the
Color Glass Condensate (CGC) endowed with the functional, JIMWLK, evolution
equation. We explicitly construct gauge-invariant amplitudes describing
multiple odderon exchanges in the scattering between the CGC and two types of
projectiles: a color--singlet quark--antiquark pair (or `color dipole') and a
system of three quarks in a colorless state. We deduce the energy evolution of
these amplitudes from the general JIMWLK equation, which for this purpose is
recast in a more synthetic form, which is manifestly infrared finite. For the
dipole odderon, we confirm and extend the non--linear evolution equations
recently proposed by Kovchegov, Szymanowski and Wallon, which couple the
evolution of the odderon to that of the pomeron, and predict the rapid
suppression of the odderon exchanges in the saturation regime at high energy.
For the 3--quark system, we focus on the linear regime at relatively low
energy, where our general equations are shown to reduce to the
Bartels--Kwiecinski--Praszalowicz equation. Our gauge--invariant amplitudes,
and the associated evolution equations, stay explicitly outside the M\"obius
representation, which is the Hilbert space where the BFKL Hamiltonian exhibits
holomorphic separability.
