As far as I am aware, the smallest available odor sensor is a trained bee or wasp. The hymenopterans are classically conditioned to extend their tongues when exposed to a particular chemical or odor profile. Then they are restrained inside a plastic cartridge, such that whenever they extend their tongues, a tiny button is pressed.

The cartridge is then loaded into a handheld device that lights an LED whenever the insect detects the odor.

Much cheaper than trained dogs, and the purely electronic detectors are not quite as robust [yet]. The downside is that you can't exactly buy it once and keep using it for the next 10 years.

Sniffer insects have been used to detect bombs, fungal blight, cancer, diabetes, pregnancy, contraband drugs, and uranium.

Pretty small, but not cell-phone sized. https://www.amazon.com/MicrOptix-VSA-100-Analyzing-Spectroph...

Ones that detect particular contaminants can be a lot smaller, especially if they are single-use.

Possibly.

Here is an article from MIT in 2014 detailing recent discoveries and improvements in chip tech that could allow this: http://news.mit.edu/2014/wireless-chemical-sensor-for-smartp...