Polaronic effects are investigated in the two-dimensional t-J model (d
escribing Cu spins and holes of the planes in high-T-c cuprates) in th
e presence of in-plane dynamic oxygen breathing modes. We focus on the
effect of dynamic multi-phonon modes. Spin and charge structure facto
rs are computed. We found evidence for self-localization of the holes
and increased short-range antiferromagnetic spin-spin correlations bet
ween the remaining spins. This effect persists when all the in-plane o
xygen vibration degrees of freedom are taken into account. This sugges
ts that dynamic phonons could play a key role in stabilizing inhomogen
eous stripe phases or domain wall structures.