Network function virtualization (NFV) fosters innovation in the networking field and reduces the complexity involved in managing modern-day conventional networks. Via NFV, the provisioning of a network service becomes more agile, whereby virtual network functions can be instantiated on commodity servers and data centers on demand. Network functions can be either mandatory or best-effort. The former type is strictly necessary for the correctness of a network service, whereas the latter is preferrable yet not necessary. In this paper, we study the online provisioning of NFV-enabled network services. We consider both unicast and multicast NFV-enabled services with multiple mandatory and best-effort NF instances. We propose a primal-dual based online approximation algorithm that allocates both processing and transmission resources to maximize a profit function, subject to resource constraints on physical links and NFV nodes. The online algorithm resembles a joint admission mechanism and an online composition, routing and NF placement framework. The online algorithm is derived from an offline formulation through a primal-dual based analysis. Such analysis offers direct insights and a fundamental understanding on the nature of the profit-maximization problem for NFV-enabled services with multiple resource types.