What causes the sensation of taste when Dimethyl Sulfoxide (DMSO) is absorbed through the skin? 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.
Short answer
It may not be so much the direct action of DMSO on the olfactory sensory system, but the smell of one of its metabolites that is excreted via the pulmonary system and the skin after ingestion of DMSO. 

Background
Dimethyl sulfoxide (DMSO) is metabolized in man by oxidation to dimethyl sulfone (MSM) or by reduction to dimethyl sulfide (DMS) (Fig. 1).


Fig. 1. The reaction of DMSO to DMS catalyzed by DMSO reductase. source: wikipedia 

DMS is eliminated through the breath and skin and is responsible for the characteristic garlic-like odor of the breath, and taste in the mouth associated with ingestion of DMSO. These effects can become noticeable minutes after ingestion and may last for several hours (Santos et al, 2003). 

Reference
- Santos et al., Biochem Pharmacol (2003); 65: 1035-41