Having just made a batch of meringues,I am now left with lots of egg yolks, can I use them in recipes that ask for "eggs" i.e cakes and tray bakes. Is the white of the egg needed in the baking process ?
It really does depend on the recipe. Egg yolks have some protein but a lot of fat which adds flavor and makes baked goods more tender and moist. Whites are just protein which adds structure and has a drying effect.
If the particular recipe is depending on the eggs for the binding power of their protein you may not get enough by substituting just yolks. Remember that the volume of the yolks is less than whole eggs so you may see better success substituting two whole eggs with three yolks.
Some cakes will handle the reduced protein. White and yellow cakes will be ok. Pound cakes will also be fine and in fact some recipes call for only yolks. Expect your cake to be a little denser, softer, and tastier. Any kind of sponge or angel food cake won't work because they rely wholly on the protein from the whites.
Soft, rich breads will also benefit from the added fat. The breads will derive their structure from the gluten in their flour. Cinnamon rolls and rich doughnuts come to mind. A local doughnut shop is famous for the yellow color which comes from using fresh yolks.
Yolks can be used in many recipes that call for whole eggs. Look for recipes that will benefit from all the added fat. Anything custard-like, where the eggs are mixed with milk, will work very well- even better than with whole eggs in fact. Examples are custard, flan, puddings, french toast, etc. Given the season you might consider a custard-based ice cream.