I dabble in veganism, and I can understand about the oil. Not all oils may be healthy but don't think of just the oil itself think about the balance of your day. True nutrition is not just about what you eat, it is about how you eat it. Veganism is great because you may be cooking with oil but turn around and look at all of the healthy choices you are making. With animal products out of your diet, I can only assume your fat intake has been decreased dramatically. Besides not all fat is bad. If you are truly cooking with a concerning amount of oil. I would instead look at what you are cooking. If you are frying a lot, maybe try broiling.
On this thread I have seen a lot of reponses about veganism not being healthy. If you are eating only carbs, sugars and crap, yeah that's not going to work. What I suggest is get a vegan cookbook that would fit best for your life. There are tons of options. My personal fav is the Veganomicon. The key to Veganism, as in all nutrition is protein. Build your plate around your protein of choice, fill at least half the plate with fruits and veggies, and then if you want grains, do it. Remember that Veganism is actually the recommended diet by the UN. The only real struggle is b12. Take a supplement.
That may not have answered your question, but I really don't think you should sweat it. Being Vegan is hard enough. Make healthy choices about what you are putting into your body, portion control, read the labels, you will be fine.
Baby vegans, it is hard, don't beat yourself up if you accidentally eat something, just keep on going. It gets easier with time.