Concurrent data structures or classes are designed to provide safe accesses and simultaneous updates by multiple threads to shared objects in a concurrent environment, with the goal of enhancing parallelism and throughput. However, testing concurrent objects poses significant challenges due to the potential explosion of concurrency test spaces, the variety of programming vulnerabilities, and the inherent nondeterminism of concurrent test executions. In this paper, we propose an Intrathread Method Orders based Adaptive Concurrency Testing (IMOACT) framework for concurrent objects. IMOACT can capture diverse behaviors of interthread method pairs through characterizing concurrent execution contexts with intrathread method orders. Moreover, IMOACT can adaptively optimize concurrent test executions by generating scheduling sequences based on the key scheduling points visited so far, streamlining test generation and execution organically across multiple tests. Experimental case studies with typical C/C++ concurrent classes demonstrate that IMOACT outperforms baseline approaches. On average, IMOACT promotes the effectiveness of detecting concurrency bugs by 65%, and achieves a speedup of 2.43x compared to the underlying state-of-the-art concurrency testing approach.