For containers that held volatile oils like thinner, leave them out for several days to fully volatilize, then dispose of them as non-combustible waste.
Heavy technical/municipal vocabulary for waste disposal instructions. 揮発性 '(having the property of) volatility' uses the productive ~性 suffix. については '(regarding) / as for X' is the formal topic marker (stiffer than は). 放置する '(to) leave alone / leave unattended' contrasts with 捨てる 'to throw out.' 揮発させて is the causative 'make it volatilize / let it evaporate.' 不燃物 'non-combustible' is the waste-sorting category term in Japanese municipal trash systems.