I have two diagnosed SPD kids. So I have a lot of advice, but it will be disjointed advice points, okay?
Vitamins - get something that is "food-based". My favorite is the MegaFood brand, but they are pricey. But - reading their literature will give you a really good primer on synthetic versus food-based supplements
Get your son tested by an occupational therapist. In the US, this discipline is where you would go for that determination. SPDs are not unserious - if not treated, they snowball into bigger problems down the road. The treatment consists of exercises and strategies to bring the kid more into balance, and also patient education. Both on the part of the parent, so the parent understands exactly what is happening and then can make better parenting decisions (because dealing with this stuff will make you want to smack some sense into your kid on those really bad days, even though both of us wouldn't do it, but the frustration is absolutely there), and also of the kid, so the kid learns to recognize when s/he is getting out of balance and what steps s/he can take on their own. My older one now manages herself, with occasional input from me (but I am always observing - moms really never stop doing that, you know)
The gold standard here for feeding difficulties is a "feeding team evaluation". You go to a children's hospital to get this. The appointment consists of a whole clutch of therapists and doctors evaluating your kid for lots of different things: defects in swallowing, breathing, and possible organ diseases and/or malformations; psychology for any difficulties in family dinnertime dynamic; nutritionist to get a grip on how the kid's current diet is doing for him/her; occupational therapist to diagnose SPD; and a couple of others I cannot remember. I had to go this route with my younger SPD, and it is there we were diagnosed with the SPD. That one diagnosis made ALL the difference for us, because I then knew which road I needed to go down for answers.
There is a cookbook set out here, "Deceptively Delicious", by Jessica Seinfeld, and its companion book, "Double Delicious". I read my copies from a local library. This mom has really picky kids, so she makes fruit and veggie purées and hides them in everything. When her kiddos were wee, they knew nothing of it, but now they are older, they know their mom does this and seemingly do not care as their old faves are, well, their old faves. There was a lot of debate here when these books came out as to the merits (or not) of this practice, but I, for one, am simply grateful there is yet another strategy out there for feeding tough kids.
Another book - "Food Chaining" by Cheri Fraker. Amazon.com. This book is a huge resource for difficult eaters. The idea is that you take a kid's eating habits exactly where they are at, and then make microsteps in the direction which they need to go. Example: from McDonalds chicken nuggets to home-sautéed chicken breast strips. So you know your starting and ending points, and then you can better map out the between-steps. TONS of other info, and some stories of kids that will make you feel like yours is a walk in the park.
My younger SPD hates fruit, so we blend it frozen into a kind of soft-serve smoothie. She will eat glasses of this. If you want my recipe tips, just ask.
Lewis Labs Brewers Yeast Flakes - tons of vitamins, just sprinkle on food. Tan in color, nuttyish tasting, does not interfere with savory flavors, my kids approve.
Since you are posting here on the MDA, I do have to mention that there is a contingent of seriously low-veggie carnivores here who state that fruits and veggies are overrated and not all that necessary as long as you buy top-quality flesh (grass-fed, organic, etc). I happen to be a veggie lover, so that statement sits kinda askew with me, but they all say they are enjoying their best health that way - it might be something to consider.
"Yummy Greens" by Solaray (a supplement company) greens-containing chewables. My picky (but not SPD) kid loves these. In fact, all my four kids were raised with these as a part of their younger childhoods.
Sorry this is so long, but I really have had my share of struggles with kids and food, and they are all now trim and healthy and strong and well along the road of being eaters who do try new things - I have hope for yours!
I have a mantra that I have spouted for years... "If I eat right, I feel right. If I feel right, I exercise right. If I exercise right, I think right. If I think right, I eat right..." Phil-SC