In this paper, we investigate the resource allocation problem for achieving spectral efficiency (SE) and energy efficiency (EE) tradeoff with users' minimum rate requirements in hybrid multi-carrier non-orthogonal multiple access (MC-NOMA) systems which incorporate both NOMA and orthogonal multiple access (OMA) modes into one unified framework. All the degrees of freedom involved in resource allocation, including the choice of multiple access (MA) modes, user clustering, subcarrier assignment, and power allocation, are jointly considered. We first formulate the SE-EE tradeoff as a multiobjective optimization (MOO) problem with minimum rate requirement constraints. Then, considering the non-convexity of the MOO problem, it is converted into a single-objective optimization (SOO) problem by utilizing weighted Tchebycheff method. Lagrangian dual decomposition and sequential convex programming are applied to solve the SOO problem. We propose a joint resource allocation algorithm which is applicable to the general case, where an arbitrary number of users can be multiplexed on the same subcarrier. Simulation results demonstrate that users' minimum rate requirements and channel conditions have great impact on the selection of MA modes. The proposed hybrid MC-NOMA mode significantly outperforms MC-NOMA and OMA in terms of SE-EE tradeoff, and the performance gain brought by four or more users sharing the same subcarrier is minimal. Meanwhile, the hybrid MC-NOMA also shows great potential to improve the tradeoff between fairness and system efficiency.