An edge dominating set    of a graph  is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number  is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G.  The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domination value is defined.  Further, the exact values of the above said parameters are found for some standard classes of graphs.  The bounds of the co-odd (even) sum degree edge domination number are obtained in terms of basic graph terminologies.  The co-odd (even) sum degree edge dominating sets are characterized.  The relationships with other edge domination parameters are also studied.