Neural transducers offer an alignment-free framework for speech-to-text modeling, and hierarchical transducer architectures further improve multilingual joint automatic speech recognition (ASR) and speech translation (ST) by stacking a translation-focused encoder on top of an ASR encoder. However, extending hierarchical transducers to multilingual many-to-many settings remains challenging: fully shared models often suffer from negative transfer and unstable target-language generation, while training separate models for each direction is computationally prohibitive. We propose LCMA-SRT (Language-Conditional Mixture-of-Experts Adapters for Speech Recognition and Translation), which augments a hierarchical transducer with language-conditional Mixture-of-Experts (MoE) adapters. A source-conditioned MoE adapter (SRC-MoE) uses source-language embeddings to reduce cross-language interference and improve multilingual ASR. A target-conditioned MoE adapter (TGT-MoE) uses the desired target language to reduce cross-target interference and stabilize target-language generation in many-to-many ST. Experiments on Europarl-ST (9 languages, 72 directions) show that LCMA-SRT improves both ASR and ST within a single joint model, reducing average WER and improving BLEU and COMET over strong hierarchical transducer baselines. We release our code and models at https://github.com/linanjie0820/LCMA-SRT.