This paper studies the joint power and admission control (JPAC) problem for orthogonal frequency division multiplexing access (OFDMA) based heterogeneous networks. We consider a small-cell network coexisting with a macro-cell network. Small cells are not only subject to constraints imposed by interference with the macro-cell network but also by the minimum achievable rates of secondary user equipment (SUE). The goal is to admit as many SUE as possible to satisfy the minimum rate requirements while maximizing a certain network utility associated with the admitted SUE. To this end, we formulate two JPAC problems aimed at maximizing the network spectral efficiency (SE) and network energy efficiency (EE), respectively, where the latter has not been considered before. In light of the NP-hardness of the admission control and SE maximization problems, prior works have often treated the two problems separately without considering OFDMA constraints. In this paper, we propose a novel joint optimization framework that is capable of considering power control, admission control, and resource block assignment simultaneously. Via advanced convex approximation techniques and sequential SUE deflation procedures, we develop efficient algorithms that jointly maximize the SE/EE and the number of admitted SUE. Simulation results show that the proposed algorithms yield substantially higher SE/EE and admit more SUE than existing methods.