Photoshop :: Convert Drawing To Use In Large Format?

I've been drawing stuff for web pages that people come back and want to use in larger formats. Like printing on their truck, or business cards, letterheads, or even large banners.

I didn't draw them with that in mind, it's this tiny image that is made for the web and is like 72dpi. So now I have to take these things somehow and convert them to scalable vectors at 300dpi if possible, but I don't know how.
How do I take any random graphic (or a handful of layers at once) and convert it to a higher DPI and make it scalable so I can send the large tiff or even the PSD to a graphic printing company who can scale it to whatever size they like and have it still look the same?

Case in point:
I am supposed to take a logo and convert it to a basic black and white print to put on their van. So I have to take off gradients and shadows and extra stuff, but I am still left with a graphic at 72dpi and very small in size. All it is, however, is text using a standard font, but I did a custom letter that kind of flows vertically between 3 lines of text. So I have 4 layers, 3 font layers and one regular drawing layer for the custom letter. The only effect I have now in this basic version is an outer glow, with yellow color overlay.

Can I make this scalable AND with effects? Can I just convert all the layers into vector paths somehow? Or is there a way to just make this 300dpi and make it 5 times bigger and look nice?

I'm just not sure how to convert or get this ready for a printer.