There is nothing poisonous about any plant in the Helianthus (sunflower) family. In fact, sunflowers offer medicinal as well as recreational benefits. The leaves are used in herbal smoking mixtures. They offer a mild smoke and are nice used as a "bulk" part of your herbal tobacco mix. Try adding to tobacco when cutting back or trying to quit smoking.
Leaves are also used in a tincture of leaf/flowers for lunch issues, chest tightness, such as a reaction to scents or before a cough loosens. I use this tincture for my husband who has COPD and gets bronchitis every winter, that lasts for months.
Make your own roasted sunflower seeds by soaking unshelled seeds in 2 quarts of water with 1/4 cup salt dissolved in it. In the morning, drain and spread them on a kitchen towel to soak up as much extra moisture as possible.
Then, spread the dried sunflower seeds onto a dry cookie sheet and bake in a 325 oven for 30-45 minutes or until the white part of the shells start to turn golden brown. Cool and eat! I store mine in a canning jar with a screw type lid. They are a much-loved snack by adults and kids alike.
Sunflower seeds are also useful when used by people trying to beat their nicotine addiction. Browned seeds are also used as an infusion, to provide whooping cough relief.
Used for Rheumatism, the roots are outside the scope of the home herbalist, but I encourage you to seek a professional herbalist and work with them and this useful herb.
Something else that is interesting, I made a tincture from sunflower leaf and blossom, and it turned shocking pink! This unexpected color is how I gauge if my sunflower is the freshest it can be.
When harvesting sunflowers, you will notice that your hands and fingernails become sticky with resin. This is indicative of herbs that are connected with lung issues. Harvest in late summer, on a dry day when the plant is resinous. I always try to harvest before noon, but after the dew has dried on the plant. I pick leaves in one pouch, and harvest the blossom heads carefully, placing them in a basket as I go.
I do not like piling a bunch of flowers into a closed pouch, especially when it is hot weather and I am going to be walking back to the house. I find that the delicate petals get bruised when they are heaped together. Work quickly, and get your blossoms into your tincture or drying rack before they have a chance to become shriveled and damaged.
There is a market for sunflowers as above, and small herb farms may want to take note. Sunflowers are easy to grow (who hasn't popped a seed into a Dixie cup?) and they do not need extremely rich soil. Sunflowers grow rapidly. They do use a lot of potash, so rotating crops is essential for the best yield. Better yet, harvest the heads, allow the stems to dry and then burn them. The resulting potash rich ash can be returned to the location.
Your goats, cattle, and other livestock will love the seed, seed heads, stalks and leaves of your sunflowers. So be sure to plant plenty for all. I like to cut and hang some sunflowers-stalks and all, dry them and then give one to my goats in the winter as a treat. They eat every speck.
Last but not least, there is nothing more enjoyable than driving down a country road and seeing an entire field full of yellow, nodding heads of sunflowers. It's cheerful and useful at the same time!