Can I use 20 feet 2x4 studs to add a ceiling in the garage?
2x4’s at 16” o.c. spanning 18’ will not work. They’ll sag under their own weight, much less adding a layer of gypsum board. 

The Code requires a minimum live load of 10 lbs. per square foot for limited storage (maximum clear space between new floor joists and roof joists of 42”) and 20 lbs. for uninhabitable storage space. (See IRC Table R301.5.)

If you want to use 2x4’s, I’d add a mid-span support, like a 2x4 extending from the 2x4’s up to the roof joists. If the roof joists don’t align with the 2x4’s below, you can add a 2x4 strongback the length of the garage. This will give you an allowable live load of about 24 lbs. per square foot and a dead load of about 4 lbs. per square foot, (joists at 16” o.c. and gypsum board on bottom),depending on the species and grade. 

If you don’t want to use a mid-span brace, you could use 2x8’s at 24” o.c.

(BTW, your drawing shows 16” BETWEEN joists and it should be ON CENTER. Oh, and the first joist from the wall should be 16” o.c. From face of wall to its center.)