You might want to try starting a small garden and grow your own berries and vegetables - most kids will eat what "they" grow. Be mindful, not all varieties are tasty as they are bred for shelf life and being shipped 3,000 to 10,000. Johnny's is a great place for seeds http://johnnyselectseeds.com
If space is an issue you can always do your planting in containers on your deck/porch in a sunny location. Do you know that you can even grow strawberries in a large hanging basket?
Just remember that the plants will get large so use very large containers.
Get creative: you can grow baby lettuce in an old wagon he can pull it into the sunniest locations of the yard or bring it in close for watering (which when it's hot and dry will need to be done pretty much daily once the plants are established.
Or, build a "Bean Teepee" here are a couple links for more ideas...
http://www.colostate.edu/Dept/CoopExt/4dmg/Children/child...
http://aggie-horticulture.tamu.edu/Kindergarden/kinder.htm
Regarding meat... I don' blame him for refusing to eat it - the meat sold in stores does not even resemble the meat our ancestors ate. Besides, it's full of hormones, not nutritious because the animals never get eat a blade of grass or an insect, most never even see the light of day.
Search for a local source of meat where the animals have been "grass-fed." Grass eating cows, for example, are more nutritious, have a proper ratio of Omega 3's to Omega 6's - which most Americans are deficient. You can learn more about meats, soy and so forth at: http://www.westonaprice.org/splash_2.htm
Buy the way, I don't eat store bought meats even if they say they're organic. Organic practically means nothing these days. For example, an organically raised cow means nothing more than it was fed organic corn (which could be Genetically Modified) and soy beans - both of which the cows stomach cannot digest. Cows need to eat real grass and not grains.
Pasta is sugar, high glycemic. So are potatoes, corn, wheat, etc. So you may want to be mindful.
Do your best to NOT allow your son to eat anything that has artificial sweeteners, you will find lots of info on why it is an appalling food for us and our kids at http://www.westonaprice.org/splash_2.htm
A terrific option for replacing sugar: Agave (but make sure it's from the plant species by the name of Agave tequiliana, if it is it will be clearly stated on the label) this particular species is low glycemic and 3-4 times sweeter than sugar. Use it just like you would honey - it tastes better than honey!
And what I found helpful when my son was a tike... let him help cook Molly Katsen has some terrific children's cookbooks. There are many kids cookbooks available but most do not address food source, food quality, and only use the what I call non-foods in the stores.
A good cookbook for mom and dad is Nourishing Traditions by Sally Fallon http://www.newtrendspublishing.com/SallyFallon/index.html
I know I put way too much in this comment but just picking one thing a year from the above list will help create a pretty healthy family. If I could only do two of the above things I would grow my own lettuce and tomatoes and buy the book Nourishing Traditions.
Hope this info helps you and others.