The Wikipedia page for DMSO says:
The perceived garlic taste upon skin contact with DMSO may be due to nonolfactory activation of TRPA1 receptors in trigeminal ganglia
...and references a PLOS1 paper. That paper doesn't seem to address the topic of DMSO taste directly. My understanding is that taste is conveyed mainly through the facial and glossopharyngeal nerves, and the trigeminal nerve conveys sensation/temperature. The paper doesn't seem to explain how a nerve whose activity normally registers as sensation/temperature becomes interpreted instead as taste.