From the Msds I have, it's essentially corrosive, as expected from an amine. Not carcinogenic, but potentially allergenic (depending on individual as usual).
The maximum allowable concentration in air is 10ppm; this equals the odour detection threshold by humans.
200ppm irritate human nose and are the LCLo, 400ppm are intolerable.
The vapour pressure at +20°C is 10mmHg or 13,000ppm - that would be the concentration if air above EDA were sealed. 65 times dilution bring you to 200ppm.
EDA vapour, being hygroscopic as an alkali, should react with water vapour in air to make liquid droplets of alkaline solution. But if no humidity at all were available in air, the EDA vapour woud find it in the lungs anyway.
If someone plans a rocket fuel with high H/C ratio to avoid sooting, EDA plus guanidine looks like the best replacement for methylamine.
For rocket fuels of normal use, tertiary amines are better, since their liquid range improves. Methylating all amine functions at once is cheap. Then, heavier compounds like pentamethyl-diethylene-triamine (PMDETA) are not volatile hence not flammable. Propylamines should improve the liquid range further, if they keep the magic in farnesane and phytane.