How can I get enough calories and nutrients on a vegan/vegetarian diet without loading up on fats, grains, or legumes?

Thats a tough one. Most veggies have so few calories in them that they are considered "free" in most weight loss diets.
Its the higher carb veggies that must be eaten more carefully.
I think most all vegan/vegetarian diets are high carb, high fat(from nuts, avacado, coconut oils, etc)
You will just have to count the calories a bit till you get a handle on it.
Frankly I wouldn't worry about the legumes. Besides carbs, they have lots of fiber which offsets the high carb factor. The real culprit in carbs is the simple ones that offer little or no nutrients along with the carbs.
Chips, snack crackers, cookies, candy, cake, pies, high sugar beverages(including fruit juice)

Well you can always eat/drink things like soda that has lots of calories...

I agree with what you've said, but at the same time, some foods in moderation are not that anti-healthy. Have you read Cordain's paper on grain being a two-edged sword?
thepaleodiet.com/research/

There are only three macronutrients: protein, carbs, and fat. You've probably learned it is easy enough to get protein from veggies. The general health of a carb is measured by its glycemic index and load or insulin index and the other nutrients it provides. Fats are actually essential to the human body, especially the brain and central nervous system. Getting healthy fats and keeping them a reasonable portion of the diet becomes key. Tree nuts and a variety of some seeds are about the healthiest source I've found.
http://www.westonaprice.org/know-your-fats/skinny-on-fats
http://www.notmilk.com/kradjian.html
www.nutgrowing.org/tree_nuts_and_health.htm

Most foods will have some negative aspect, so this also becomes an exercise in finding ones that are better than others. A diet consisting mostly of a variety of organic, non-GMO, raw veggies is about the most general way to eating healthy. You may research ORAC values, nutritional density, and nutritional data. For each nutrient, research good sources. Then look for ones that have more of them.
www.drmcdougall.com/misc/2007nl/apr/protein.htm
michaelbluejay.com/veg/protein.html
http://www.pcrm.org/health/diets/vsk/vegetarian-starter-kit
nutritiondata.self.com/
oracvalues.com/
www.drfuhrman.com/library/article17.aspx
www.cdc.gov/pcd/issues/2014/13_0390.htm

Here are sites I use for food ideas. Just type in an ingredient or dish name, add vegan to the list for health.
www.yummly.com
allrecipes.com
engine2diet.com/recipes/favorites/
www.nomeatathlete.com/rice-and-beans/

10 cheapest, healthy foods per the Bureau of Labor Statistics, U.S. Department of Agriculture, Centers for Disease Control and Prevention and WebMD.
www.thestreet.com/story/12837794/1/the-10-cheapest-health-foods-money-can-buy.html?puc=yahoo&cm_ven=YAHOO
oats, dried beans, eggs, brown rice, popcorn, cabbage, onions, bananas, watermelon, beets

Rip Esselstyn @ TED, former firefighter and 12yr professional tri-athlete, food that satisfies Texas-beef guys, dropping weight and their cholesterol by 60pts.
engine2diet.com/recipes/favorites/
http://www.youtube.com/watch?v=AAkEYcmCCCk

Books: Engine 2 Diet, The Natural Way to Heal, Formula for Health (raw), Wheat Belly, Grain Brain, Fit for Life

Q: In need of good healthy meal ideas?
https://answers.yahoo.com/question/index?qid=20140522135458AA1jGBX

Q: What kind of sandwiches?
https://answers.yahoo.com/question/index?qid=20140523085301AARHQi2

Q: Cheap and healthy snack ideas?
https://answers.yahoo.com/question/index?qid=20140508155000AAFX3lN

Results of Best foods: Amazing 70yr old woman vs typical USDA food results, using her backyard
www.youtube.com/watch?v=qj7dhoHpyssf

How Monsanto is impacting the world, why it's voted the most evil corporation in the world. How does that effect your health?
http://www.youtube.com/watch?v=N6_DbVdVo-k

The Paleo diet explained. The part I'm not on board with is the exclusion of wild and organic brown rice, and organic corn. Soy has the estrogen and 90% GMO issues. However, the major points he covers are true from all that I know. Even if eating vegan, the nutrition explanation and potential shortages in diets is good to know.
https://www.youtube.com/watch?v=52A3ayfxfTs

DEBATE: Cave Man Vs. Vegan: What is the Best Diet
https://www.youtube.com/watch?v=ery6ez2M7aw

Books: Engine 2 Diet, The Natural Way to Heal, Formula for Health (raw), Wheat Belly, Grain Brain

Hope these help. Take care and have fun!

pasta and potatoes with the fresh vegs and fruit instead of grains provide some carbohydrates. protein and fat also in pastas - (made with) egg more of both. breads also vary in fat and additive content as well as the variety of grains used for their flour.

Quinoa is a grain that is very high in protein. Chips / fries - high in calories.

Use olive oil for cooking and also as a dressing on salads. It is also a healthy fat.

Avocados - high calories, loaded with good fats and nutrients.