If I want a DIN font style, I usually use either:
DIN17SBOP-Regular
or
DIN17
However neither of these have Greek characters. Is anyone aware of one?
Parachute Fonts' DIN supports Greek, and FF DIN "partly supports Greek". The main difference you'll see is in the italics. PF DIN uses a true italic with a handwritten feel, FF DIN has a sloped roman oblique.
Seemingly you have got a couple of usable suggestions in another answer. If it happens that you must use freeware you can try a trick. There's a free CAD program which contains a couple of fonts which resemble thin DIN style fonts. After installing the program the font appeared also in other Windows programs.
There's no real Bold nor Italic versions, they are available only in programs which create them mechanically by thickening and slating the regular version.
CAD program: DesignSpark Mechanical
Fonts: SpaceClaim ASME CB and SpaceClaim ISO CB
The glyph list shows this Greek and Coptic section: