Is There An Alternative To Using Mesh Or Silk In Screen Printing?

If you want a "screen print" you'll need to use some kind of mesh, but there are all kinds of mesh. Check out some of the info and links in my answers here:
and (all 6 Image Reprod. bds)

You can so various kinds of stenciling or masking though to create prints that won't involve a "screen" or mesh ...just a few:
...or use your own "masking" fluids or other materials
(also see more in Image Reproduction boards link above)

How Do You Silk Screen Print Using Oil Pastels As A Blocking Medium?
I Saw In A Book A Way To Use Oil Pastels On The Screen To Keep The Ink From Soaking Through The Screen, But I Can'T Find Anything Online. Anyone Have Any Good Tutorials?

indeed you can, its a monoprint technique. You carefully draw on the screen with the oil pastel and then pull your ink across it, wherever you've drawn you should have a clear area. Keep in mind that you need to be gentle when drawing on the screen so as not to damage it, but press hard enough so that you fully block the screen. The difficult part with this method is that you can't remove the pastel with water and soap, you have to use solvent (either turpentine or mineral spirits) Being as how you can't flush solvents down the drain, you have to dispose of them properly and carefully, it makes this technique a bit difficult if you don't have the right surroundings.

So, that in mind, heres a few other similar options: speedball screen filler, you can paint it onto your screen and wash it out chemical free
caran d'ache or chalk pastels can be used to make positive images on a silk screen as well, you draw on the screen with the crayon or pastel and then pull a clear ink over the drawing. The pigment of the crayon/pastel will carry through the screen with the clear ink to create a print. Its a very fun and organic way to print, I've had a lot of success using this particular method.