Neuro-symbolic NLP methods aim to leverage the complementary strengths of large language models and formal logical solvers. However, current approaches are mostly static in nature, i.e., the integration of a target solver is predetermined at design time, hindering the ability to employ diverse formal inference strategies. To address this, we introduce an adaptive, multi-paradigm, neuro-symbolic inference framework that: (1) automatically identifies formal reasoning strategies from problems expressed in natural language; and (2) dynamically selects and applies specialized formal logical solvers via autoformalization interfaces. Extensive experiments on individual and multi-paradigm reasoning tasks support the following conclusions: LLMs are effective at predicting the necessary formal reasoning strategies with an accuracy above 90%. This enables flexible integration with formal logical solvers, resulting in our framework outperforming competing baselines – by 17% and 6% compared to GPT-4o and DeepSeek-V3.1, respectively. Moreover, adaptive reasoning can even positively impact pure LLM methods, yielding gains of 10%, 5%, and 6% on zero-shot, CoT, and CoT_sym settings with GPT-4o. Finally, although smaller models struggle with adaptive neuro-symbolic reasoning, post-training offers a viable path to improvement. Overall, this work establishes the foundations for adaptive LLM-symbolic reasoning, offering a path forward for unifying material and formal inferences on heterogeneous reasoning challenges.The code and data are available at https://github.com/idiap/adaptive_symbolic_reasoning.