In this paper, the relays' intrinsic available resource and the extrinsic incentive mechanism affect its behavior of forwarding multi-service (i.e. different types of many traffic streams and different priority classes of one traffic stream) in selfish wireless networks (SeWNs). The node-selfishness information (NSI) of the selfish relay node includes its degree of node-selfishness (DeNS), its degree of intrinsic selfishness (DIS) and its degree of extrinsic selfishness (DES). The relay's DIS is defined as the effect of its own residual energy on its node-selfishness, whilst its DES reflect the relationship between the incentive mechanism and its node-selfishness. Based on the relay's NSI, the expected energy cost (EEC) and the expected service profit (ESP) is determined for analyzing the multi-service forwarding of the relay node, and an optimal incentive factor paid by the source node is obtained for effectively delivering multi-service. Our simulation results demonstrate the effective multi-service forwarding with the relay's NSI.