Online social media platforms are central to everyday communication and information seeking. While these platforms serve positive purposes, they also provide fertile ground for the spread of hate speech, offensive language, and bullying content targeting individuals, organizations, and communities. Such content undermines safety, participation, and equity online. Reliable detection systems are therefore needed, especially for low-resource languages where moderation tools are limited. In Bangla, prior work has contributed resources and models, but most are single-task (e.g., binary hate/offense) with limited coverage of multi-facet signals (type, severity, target). We address these gaps by introducing the first multi-task Bangla hate-speech dataset, BanglaMultiHate, one of the largest manually annotated corpus to date. Building on this resource, we conduct a comprehensive, controlled comparison spanning classical baselines, monolingual pretrained models, and LLMs under zero-shot prompting and LoRA fine-tuning. Our experiments assess LLM adaptability in a low-resource setting and reveal a consistent trend: although LoRA-tuned LLMs are competitive with BanglaBERT, culturally and linguistically grounded pretraining remains critical for robust performance. Together, our dataset and findings establish a stronger benchmark for developing culturally aligned moderation tools in low-resource contexts. For reproducibility, we will release the dataset and all related scripts.