My air vent is blowing out some sort of gas/dust that leaves a green film on my windshield, it doesn't matter if the A/C is on or off. It also has a weird smell.

You could also bypass ur heater core the only thing is that you wont have hot air but if you live in az like me you really dont need it.its pretty simple open ur hood look towards the back of the engine (fire wall) left side there should be two hoses going in ur car one is cool antifreeze going in ur core and the other is hot antifreeze coming out jus cut those hoses wright when there going in the firewall and connect them together.and u jus bypassed ur heater core.if ur having this problem ur probably low on antifreeze in ur radiotor u should check it.

You have a leaking heater core. This can leak whether you are using the heater or not. Heater core replacement is pretty simple, except that in many cases you must remove the dashboard to gain access to the core. This can be a major undertaking.

What model year is your S-10?

Good Luck!