Three heterometallic one-dimensional (1D) coordination polymers {A[CrCu2(bpy)2(C2O4)4]·H2O}n [A = K+ (1) and NH4+ (2); bpy = 2,2'-bipyridine] and [(Cr2O7)Cu2(C2O4)(phen)2]n (3; phen = 1,10-phenanthroline) with uncommon topology have been synthesized using a building block approach and characterized by single-crystal X-ray diffraction, IR and impedance spectroscopies, magnetization measurements, and DFT calculations. Due to the partial decomposition of the building block [Cr(C2O4)3]3-, all three compounds contain oxalate-bridged [Cu2(L)2(μ-C2O4)]2+ units [L = bpy (1 and 2) and phen (3)]. In compounds 1 and 2 these cations are mutually connected through oxalate groups from [Cr(C2O4)3]3-, thus forming ladder-like topologies. Unusually, three different bridging modes of the oxalate ligand are observed in these chains. In compound 3 copper(ii) ions from cationic units are bridged through the oxygen atoms of Cr2O72- anions in a novel ladder-like mode. Very strong antiferromagnetic coupling observed in all three compounds, determined from the magnetization measurements and confirmed by DFT calculations (J = -343, -371 and -340 cm-1 for 1, 2 and 3, respectively), appears between two copper(ii) ions interacting through the oxalate bridge.