In general, I highly recommend this Wikipedia page when it comes to trying to figure out the sizes of armies in Middle Earth. It compiles all sorts of little mentions of battalions, hosts, regiments, etc., and gives a more understandable summary view.
So, that being said, here’s what I can tell you about the armies at Helms Deep and the Pelennor Fields:
It’s mentioned twice in the books that Saruman’s army at Helm’s Deep is made up of at least 10,000 orcs. This number does not include the other members of Saruman’s army, though - men, wolves, and half-orcs. So the final number would have been at least a bit above 10,000 (this is only the army attacking Helm’s Deep, by the way. Saruman had nearly another 10,000 soldiers stationed elsewhere.) As far as being enough to destroy men: keep in mind that, while the actual population numbers for Middle Earth are never given, it’s implied that there are not a whole lot of men around to be destroyed. So 10,000 could have been plenty enough to do the job.
It’s also worth saying that, before the war started, Saruman and Rohan were pretty evenly matched - both, in total, had about 20,000 men. But Saruman’s advantage came from the fact that he acted first, and in the two battles of the Fords of Isen as well as the initial attack against Helm’s Deep, Rohan loses about 5,000 men. Which put them at more of a disadvantage by the time the battle of Helm’s Deep comes around.
The Pelennor Fields
After Rohan fights their war with Saruman, Theoden can only spare 6,000 men to ride to Gondor’s aid (don’t worry about the movie - their job is to look awesome, not necessarily accurate.) They joined 3,000 men that came in from outlying provinces to support Minas Tirith. When Aragorn arrives, he brings about 4,000 more men. This was in addition to the men already stationed at Minas Tirith (and the survivors from Osgiliath) - their exact numbers aren’t given, but are estimated to be around 5,000 in total. So, altogether, Gondor was defended by an army of about 18,000 men.
Meanwhile, Mordor’s army is not described in exact numbers. But, based on the comparisons given in the book (for example, saying that the Rohirrim were outnumbered “ten times and more than ten times”), it’s estimated that the entire army numbered at around 75,000. This was a combination of orcs, trolls, wargs, oliphaunts, and a ton of men from the south and east. But the extreme advantage that Mordor had over Gondor explains why it’s so impressive that Gondor won (and without any unstoppable ghost army, thank you very much Peter Jackson.)
SOURCES: LOTR, “Armies and Hosts of Middle Earth Warfare" on Wikipedia