I have never tried to grow veggies in straw bales. I did -- once -- try to use straw bales as mulch. They sprouted, and I had more weeds than veggies that year. Perhaps there's a trick to straw bale gardening of which I'm unaware.
As for shady raised beds -- how shady are we talking here? Do the beds receive any sun at all? If so, for how long and what time of day?
For example, if your beds get a few hours of morning sun but are shaded in the afternoon, they might work well for a number of spring crops that tend to suffer during our early spring heat waves. That would include lettuce, spinach, beets, radishes, onions, and carrots. And if sun hits it for four hours or more, peas and potatoes might well survive also. I've also found that shady raised beds are ideal for asparagus. And I've known a few folks to grow celery in such locations, although I've never tried it.
Summer vegetables pretty much all need more heat and sunlight than you apparently have. But you could grow shade-loving herbs in such areas. If your raised beds are contained, you could have mints, for example, without fear of having them escape to other areas. Parsley and tarragon also like to avoid our summer heat. And my lemon balm grows well in a shady spot.
