From what I can scrounge, it seems that France and Germany in the world wars ended up using about a third of their male (fighting age) population. As a rough estimate, that's about 11% of their total population. Of course, that's not counting all the boys and really old men who ended up fighting, including the Hitler youth towards the end of the second world war.
So the question is, how would the goblins compare to this?
Now, these examples are humans, in a modern industrial nation, which needs workers to keep making the ammo and farming the food for their armies (unless you're like North Korea, and you just stockpile that stuff ahead of time). If they were a barbarian tribe, burning their own fields as part of an oath to win or die, then you'd be able to muster most of your male population.
But with these goblins... they have a larger workerbase, too. Let's look into that.
Using US population numbers, about 66% of the population are adults of 15 to 64 years, 14% are 65 or older, and about 20% are children of 0 to 14 years.
Using Nambia's population, you get 59% adults, 4% of people 65+, and 37% are 0-14.
We'll say goblins have 40% kids of 0-14 due to high fatality and birth rates. That'd leave 56% adults, and 4% elderly.
Goblins don't grow old, so that's an extra 4% of the population for labour, making it 60%.
We'll say working age starts at 7 for a goblin. That's means half of the 0-14 age bracket is added to their work force (that is an extra 20% of the population). That makes it 80%.
So while the USA has 66% of its population of working age, goblins have 80% of theirs of working age. That means for every five American workers, the goblins have six (per capita).
Replacing Women at Home
Something the Germans are often criticized for in the world wars, is not making use of their women in the war effort. Which is silly... the women were doing a lot of the farm work and other jobs necessary to keep a civilization working, the Germans had already exhausted all extra hands.
So, even though goblins have twice the available potential recruits, that doesn't necessarily mean twice the army size. Who is going to farm? Who will care for their kids and babies while they're away? Who will have children to replace war losses? If you send out all available adults, you better win that war fast--or your community will be destroyed.
You can get around some of this by details like having group homes for children, and wrangling up the infirm and too young goblins to perform various jobs. They won't perform them well, but then do goblins ever perform them well?
If half the population must stay at home
So, if we assume Germany could not spare one woman to fight (not without a man taking her place at home), we're looking at 13.34% of the goblin population able to fight.
On the bright side, the goblins have twice the recruiting pool to pick from, to increase the quality of their troops.
That is... if goblins ever do make quality troops.
If a Third of Women can Fight
Conversely, if you assumed that the Germans could've drafted a third of their working age women to fight, as well as a third of their working age men, then you'd be looking at an army of 26.67% of the goblin population, over a quarter.
Total War Population
So, if pushed to World War extremes, the goblins can probably muster between 13% and 26% of their population, depending on how you handle that last question. In the larger case, that's over twice the amount humans can muster (per capita). And in the smaller case, that's 118% of human troops.
But we have another variable we'll want to add to this:
But now we need to consider people unable to work or fight due to medical conditions.
From what I can find, between 10% and 30% of the working age population is physically or mentally disabled, in modern states and countries.
The goblins, having poor medical care, health issues, work-safety issues, ought to have a high percentage (most would only be missing fingers or such, reducing their work efficiency but still letting them work).
At the same time, though, goblins disdain their weaker members. So we ought to see a lot less cripples, who end up starving or even being killed. Those disabled goblins who remain are probably tough as nuts and good at an occupation, or are living on the edges of society (virtually dead, to the system).
We could even try to calculate how much of the population is effectively lost to minor disabilities. Where, if ten goblins work 10% slower due to lost fingers, that's the same as having one less goblin, in theory.
In the end, I'll say goblins have 15% of their working population in cripples.
So 80% - 15% = 68%. 68% / 3 = 22.67% War population, or 11.335% if half the population must remain at home.
You can adjust the percentage of cripples in their society (Nazi goblins who kill off their cripples, for instance) to get different results. Even up to half the goblin population being crippled, so that only 13% of the population can be brought to war.
North Korean Method
And if they did decide to be like North Korea, and have all the able bodied persons fighting (using stockpiled food and ammunition etc):
At 15% cripples, that means a few months with about 68% of their population fighting.
Of course, that doesn't take into account things like the local garrison, caretakers for the children, and people needed for other jobs to stop your cities becoming inhabited with wild beasts and mildew.
Looking at North Korea, they apparently plan to raise about 30% of their population, relying on stored ammo and food.
By my reckoning, the goblins could muster between 26% and 11% of their population. Depending on how many people they want to stay at home, and how many have infirmities.
If they decided recruit their farmers and factory workers, relying on stockpiles of ammunition and food to fight, they might muster anything between 68% and 80%.
And that compares to an estimated 11% of the population, for industrial humans in a total war scenario. North Korea from what I hear plans to raise almost 30% of its population for war, by using stored food and ammo.
NOTE: This is for a World War/Total War situation. For smaller conflicts, armies tend to consist of much smaller percentages of the population.