Detecting toxicity in online multimodal environments, such as memes, remains a challenging task due to the complex contextual connections across modalities (e.g., text and visual), which demand both common-sense reasoning and contextual awareness. To bridge this gap, we propose a hybrid neurosymbolic framework that unifies (1) distillation of implicit contextual knowledge (e.g., sarcasm, cultural references) from Large Vision-Language Models (LVLMs) and (2) infusion of explicit relational semantics through sub-graphs from Knowledge Graphs (KGs). Experimental results on two benchmark datasets show the superior performance of our approach, Knowledge-Infused Distilled Vision-Language Model (KID-VLM), over the state-of-the-art baselines across AUC and F1, with improvements of 0.5%, and 10.6%, respectively, in HatefulMemes Benchmark across variants. Further, KID-VLM demonstrates better generalizability and achieves the best performance across all baselines in the HarMeme Dataset with a 6.3% and 3.2% in F1 and AUC.Given the contextual complexity of the toxicity detection, KID-VLM showcases the significance of learning compact models (~500M parameters) from both explicit (i.e., KG) and implicit (i.e., LVLMs) contextual cues incorporated through a hybrid neurosymbolic approach. Our codes and pretrained models are publicly available.