New bread maker asks: how to make a bread loaf stay 'firm and solid' without a loaf pan?
You are spot-on: Whole-grain recipes often use more water and tend to "flow", so using a loaf pan is typically the way to go. Loaf pans alow for a "wetter" dough. 

It is absolutely possible to bake a free-form whole-wheat loaf, but it needs experience with kneading, resting time and shaping to balance the water content and comparatively low gluten. Also, for the final rise you had better not rest it on the counter, but in a floured basket (in a pinch, a bowl will do) to avoid the "flattening" effect you noticed. Bake in a very hot, well-preheated oven on a hot pizza stone or in a hot dutch oven to encourage proper crust formation and a good oven spring in a humid environment. (Unless you are going for the solid "Pumpernickel" type, but that would be in a loaf pan anyway.)

So find another recipe (or experiment yourself if you have the experience) and you are good to go. I have successfully worked with high water content (up to 80%), but always with a poolish/pre-fermentation with a long slow rise to "soften" the whole-wheat and get the enzymes going. Doing a few rounds of stretch-and-fold during the first rise helps to align and strengthen the gluten structures (and a tablespoon or two of additional gluten ("vital wheat gluten") is a good trick up your baker's sleeve as well...). Sourdough is optional if you are baking wheat-only, but if you use rye, you should definitively look into that subject as well.

If your main goal isn't a whole-grain loaf, use a classic "Artisan bread"-type recipe, and start exchanging some of the white bread flour with equal parts of whole wheat flour (and - optionally - add some gluten). Find your personal ratio where the result satisfies you. For 20-30% whole-wheat you won't notice much of a difference, with 50% your loaf will get denser and possibly need some "tweaking", e.g. a splash of extra water. The "long-cold-rise-with-very-little-yeast"-types are the most flexible in my experience.

(The oil isn't a problem.)