Orthogonal frequency division multiplexing - integrated sensing and communication (OFDM-ISAC) has emerged as a key enabler for future wireless networks, leveraging the widely adopted OFDM waveform to seamlessly integrate wireless communication and radar sensing within a unified framework. In this paper, we propose adaptive resource allocation strategies for OFDM-ISAC systems to achieve optimal trade-offs between diverse sensing requirements and communication quality-of-service (QoS). We first develop a comprehensive resource allocation framework for OFDM-ISAC systems, deriving closed-form expressions for key sensing performance metrics, including delay resolution, Doppler resolution, delay-Doppler peak sidelobe level (PSL), and received signal-to-noise ratio (SNR). Building on this theoretical foundation, we introduce two novel resource allocation algorithms tailored to distinct sensing objectives. The resolution-oriented algorithm aims to maximize the weighted delay-Doppler resolution while satisfying constraints on PSL, sensing SNR, communication sum-rate, and transmit power. The sidelobe-oriented algorithm focuses on minimizing delay-Doppler PSL while satisfying resolution, SNR, and communication constraints. To efficiently solve the resulting non-convex optimization problems, we develop two adaptive resource allocation algorithms based on Dinkelbach's transform and majorization-minimization (MM). Extensive simulations validate the effectiveness of the proposed sensing-oriented adaptive resource allocation strategies in enhancing resolution and sidelobe suppression. Remarkably, these strategies achieve sensing performance nearly identical to that of a radar-only scheme, which dedicates all resources to sensing. These results highlight the superior performance of the proposed methods in optimizing the trade-off between sensing and communication objectives within OFDM-ISAC systems.