How many oak 2x4s can you glue together the long direction before the width span is too weak?

Aside from weight, you're looking at a HUGE amount of expansion and contraction. It literally could destroy your bed.

Not sure who mentioned foam core - but that's a vastly better idea than 2x4's or sixes. PLUS, to glue up those boards you have to plane the edges. They MUST be flat, straight and true or you'll end up with gaps. and those gaps will be weak points. Plus, if you use wood it must be absolutely check free (no cracks) or it'll split faster than a drunk on payday.

But rather than using foam core and 1/4 inch ply I'd opt for fiberglass over foam. No hydroscopic (moisture absorbing) issues, easier to work with and can be molded to match whatever contour you may have or desire. Plus, it'll likely be in the realm of 20 to 50 pounds, versus what I suspect would be close to 500 pounds.

Assuming a 2x4 board 7 feet long might way 35 pounds, if you have 18 of them, 18x35=630 pounds If you go with 6 feet, assuming 30 pounds that's still 540 pounds. A LOT of weight in deed.

Fiberglass will be easier to paint. Any damage can be more easily repaired. You can cut and sand the edges to match exactly what you want, patch it with more fiberglass, sand it and paint it and end up with a professional looking cover. All wood? Might look great when done but it won't last. And to stiffen it up across the bed you'd probably have to run cross beams. And that will hamper expansion and contraction. Hence, even more trouble with the wood cracking and splitting.

Wood? No. Don't go that route. Fiberglass or carbon fiber if you know how to work it. I've never worked carbon fiber, but I wouldn't mind learning one day.

That's a pretty heavy tonneau cover. Don't forget that you have to lift it. You could easily expect a tonneau made of solid 2x4 to weigh over 100 lbs.

Consider a foam core laminate construction instead. Your bottom layer would be 1/4" plywood, the middle is 1/4 - 1/2" foam board, and the top is another 1/4" plywood. Then you can apply a thin skin of whatever material you want to get a nice appearance. That should come in weighing less than 50 pounds total.

it will be a heavy cover

you should use white oak instead of red, because of the closed cell structure white does better in outdoor applications than its red counterpart with open cells

with wood being a hydroscopic material you will have to deal with expansion and contraction issues inherent to wood, maybe seal it completely with clear fiberglass to limit this

as far as strength that will depend on how well they are glued together, wood glues are stronger than the wood itself but if the surfaces aren’t well prepared, mate well and properly clamped then the joints will be weak

I would use one inch boards with cross bracing underneath. You will need to true them up on a table saw and it would be a good idea to use a biscuit cutter and biscuits when gluing them together and then clamp them. It's going to be heavy and very costly to do. Go to a flooring store and check out oak flooring. It's grooved for a nice tight fit and would be easier and cheaper to do but you will still need something under it for bracing.

glue won;t very long, especially outdoors - why wouldn't you use screws or nails?