[Kuruharan]

1000 Elf spearmen (presumable a similar number of archers)

Another thing that puzzles me is why every always latches onto this 1000 spearman thing as if presuming that the Elvenking launched all his melee forces at the goblins in that initial attack...when mere sentences later it says that the elves charged again "with renewed numbers." And then after many of his spearmen charged with Thorin, the Elvenking was still able to make a formidable stand on Ravenhill. I think the estimates of the Elves could probably need to be raised a bit and the numbers of Men also in proportion.

Anyway...

Thorin states in the Hobbit that the Dwarves of Erebor did not feed themselves rather they depended on lucrative trade to bring in their foodstuffs.

So did many cities of antiquity and the medieval period who did not have enough farmland in their immediate area to support their populations...and some of these cities were very large indeed (Rome, Alexandria and Constantinople immediately leap to mind). There is nothing there to guide an estimate of dwarven population, certainly not enough to consider it to be a limiting factor by default.

Thereafter no mention is made of large Dwarf hosts, even during the War with the Orcs that army was of all seven Dwarf houses. For us who wish to believe in large Dwarf armies (believe it or not I am one) it would help if there was at least one referece or example of one in the Third Age.

Our accounts of the War of the Dwarves and Orcs are scanty at best. Understandably enough, given the topic at hand, you seem to be looking for Tolkien to give specific references to numbers in his works, that just isn't something he did very often. We have to instead rely on some common sense and guesstmiation based on the things he did say and the parallels we can draw to events in our own world.

Just to gain some perspective, the numbers I am proposing could hardly be considered "large" in an absolute sense. They certainly are not large in comparison to the forces I'm proposing to array against them. They are only large in comparison to the paltry handfuls others seem willing to assign them. Handfuls which to me seem too extreme given the nature of the strategic and tactical situations based upon the things Tolkien did tell us about the war in the North.

but even if the men from Dale were half as strong as he was, three days of fighting against unreasonable odds would be possible. Furthermore, even if they were regular men, it would be possible if the terrain was just right! As far as I know, it is not told WHERE the battle took place, perhaps King Brand was a master strategist who managed to funnel the enemy somewhere their overwhelming numbers were useless.

That really didn't work so good in the Battle of Five Armies, though. That one only lasted about half a day.

And it depends on which battle you are referring to for King Brand to be a strategic genius. If you mean the battle out in the plains where he was driven into Dale...the land out there seems flat and without choke points. If he'd fought out there outnumbered by more than 2:1 he wouldn't have made it back to Dale at all, he would have been swallowed whole.

If you mean the three day Battle of Dale itself, we are told that it was fought "around the mountain's feet" and I really rather doubt Brand was calling the shots at that one.

Furthermore, I don't know where that quote came from, but it was said here that about half the forces in Pelennor were orcs (the rest thus being men).

I don't recall that quote either.

But lets assume that is true. It is certainly true that Sauron's orcs didn't put up much of a fight once they were flanked by Aragorn. If I recall correctly it was the Easterlings and Haradrim who were mainly described as putting up most of the fight in the Pelennor fields. However, if you take the orcs out of the equation as being a routing rabble (which does seem plausible)...you are suddenly left with Sauronic human forces that certainly don't outnumber the repeatedly reinforced forces of the Free Peoples nearly as much as had at the start. They may not have been much more numerous at all, probably not to the point of even 2:1 at that point. Given the superior (and greatly buoyed by two improbable saves) morale and the superior weapons of the Gondorians and Rohirrim, its hardly surprising they won the battle. Even so the battle was described as fierce and many Gondorians and Rohirrim were killed in it.