Vegetarian household kitchen grey water, veg oils, dairy-ok for plants and soil? Or not.

hi
I'm a newby to grey water. Advice would be appreciated.

We live in a community situation with 15-40 people. Totally vegetarian kitchen. We use veg oils, eggs and dairy tho- we want to water one of our gardens with our kitchen water. The garden does have herbs and veggies. We got Oasis soap, supposed to be safe for plants and soil. Still, we're conservative with the soap.

We use veg oils (canola,olive, avocado, safflower) and mayo, cheese, milk, eggs etc. is this stuff ok for plants and soil? That's my main question.

We've been doing it with a barrel we empty the water from the kitchen to. Small scale at the moment because it's still experimental, maybe 5-10 gal per day.

Barrel has spigot & 3/4" irrigation hose setup that goes to a few veg and herb plants and a few flowers and trees. It's on a hill so gravity brings the h2o down the hill thru the hoses which have holes at base of plants. There is a screen in the hole we pour water into as a filter. We clean the screen periodically. Any advise?

Sounds like a simple workable system to me. The only likely problem would be if the water sits too long in the collection barrel it could develop a funky smell. This won't harm the plants, but it might be unpleasant to be in the vicinity.
I wouldn't in general use greywater on salad crops.....things to be eaten raw that the water will come into contact with. Stuff up off the ground, that the water never touches, and things that are to be cooked, no problem.
You might move up to a direct drain system where the kitchen sinks drain downhill to planted areas.....perhaps trenches filled with woodchips or gravel, and then plant your plants roundabout. You could set up several of these and switch the drain hose from one to the next on different days, too. Anything to not have to tote heavy buckets of water around!