We present a scanning tunneling microscope study on reactivity of chemisorbed oxygen on the Cu(110)--(2 \ifmmode\times\else\texttimes\fi{} 1)--O surface. We have found that the Cu(110)--(2 \ifmmode\times\else\texttimes\fi{} 1)--O surface is intrinsically unstable under thermal annealing in the 400--900 K range. In the 455--570 K range, the surface undergoes faceting. The orientational transition of the adsorbed oxygen phase displays wide [110] terraces, covered by (2 \ifmmode\times\else\texttimes\fi{} 1)--O bands self-assembled into a superstructure, as well as bunches of oxygen-free narrow terraces. We found that the wide [110] terraces are intrinsically unstable against further restructuring at their edges. The restructuration is driven by reversible thermal dissociation of the (2 \ifmmode\times\else\texttimes\fi{} 1)--O bands. The slightly uneven oxygen band density between terraces, consequently differing in reactivity with respect to Cu--O fragments, induces Cu atom transport between their edges. The interplay between thermal dissociation of the (2 \ifmmode\times\else\texttimes\fi{} 1)--O bands and long-range elastic relaxation of the strained surface is suggested to be the origin of the observed inhomogeneous oxygen distribution. In the 570--810 K range the Cu atom transport reveals continuous growth of the oxygenated [110] terraces. We discuss in detail the mechanism of the Cu transport, which results in a rapid propagation of the oxygenated terraces as well as a strain development on the surface.