Leeks
Cooking: These are not eaten raw. The white and light green part is sweet and used in many dishes, while folks tend to use the woodier green parts in stocks. Some people indicate the dark green leaves are not edible, but I use all the parts and just take extra care in cooking the green parts longer so they are softer. I use leeks in soups, stews, and stocks. You can also stir fry all the parts of the leeks, or make a leek side dish. I have also seen the dark parts split and laid out steamers under the food you are steaming; to impart some flavor, also consider putting under fish or chicken while you bake them, etc.
To Clean: Always wash leeks, even if there is indication it has already been washed. Do this by cutting off the roots. Cut the leeks in half lengthwise. Wash under a running tap, with a colander under to catch any food. Fan the layers out and rinsing away dirt and grit that is often trapped between the leaves.
Storage: I keep them in a bin in the fridge wrapped in damp paper towels.
Flavor: Leeks are from the Allium family (garlic, onions) and give a softer onion flavor. Unlike onions they do not caramelize and can turn a bit bitter if you try to brown them.
Ramps
Cooking: Ramps are young, wild spring leeks with a heavier onion-garlic flavor than leeks. They grow at higher elevations in Eastern North America. The tops are milder than the white bottoms. Use on the grill, pickle, in omelets or frittatas.
Storage: My experience with ramps is limited (they do not grow around here) and I have found it is easier to eat them as soon as you have them, as storage is a bit more complicated. They can loose flavor and do not dry well. Some people I know make ramp-butter or ramp-pesto as a way to preserve the flavor. But for limited storage, do not clean and put in the fridge asap as they last ~2-4 days.
Scallions
Cooking : Scallions are young spring onions before the bulb starts to grow. They have different names, but are the same plant. These can be used raw as they are a bit sweet and have no real onion bite to them. The green part is used as a topping in many dishes, the white part is incorporated into many stir fry dishes.
Storage: Break the bunch apart and rinse cold water. Pat dry with a paper towel and then wrap in the now damp paper towel. Place in a plastic bag and put in the fridge drawer. I have kept them for about a week in this state.
Spring Onions
Cooking: An older scallion, these onions have a more intense taste than their younger selves. These look like larger scallions with bulbs starting to bulk up. These are grilled, and I like them in hash were I cut them up a bit larger so you can taste them.
Conclusions
I use green onions and leeks almost every week. It is a good base for so many dishes and lends its mild taste to tender and light dishes that can be too easily overwhelmed with regular onions.
To find out more about onions or garlic please see my other articles.