I've looked on Google and Wikipedia, but all I found were Casualties, not total servicemen.
Okay, I’m going to write this up quickly so I have a rest before the CNN Presidential Debate later on today.
Millward [Milward, A.S. War, Economy and Society, 1939-1945 (1977, Penguin Books) pp. 58] states in 1977 that ‘the Second World War is...the greatest statistical gap in the twentieth century’. Even 40 years later, that statement is still true. This was a conflict on a global scale and at a time where we did not have the tools or the resources to effectively monitor all those affected.
Additionally, it’s incredibly difficult to get statistics from countries whose records may have disappeared or have never existed in the first place. This is why casualties are used, they’re the most precise measurements we have as of right now of understanding exactly how many people were affected as casualties were well recorded in the bureaucracy of the war.
So knowing that, we’ll probably never find out exactly how many people served completely, but there is a chance of making a few estimates. Some will be more accurate than others (for example, the US, who was never invaded and never destroyed their archives in contrast to Germany who saw documents shredded or lost during and after the war).
Never the less, I found some sources that estimate troop numbers that may help to answer your question, but I cannot vouch for their validity.
In total, 690 million people served in WWII [according to Statistic Brain].
The difficulty now is at what times and in what circumstances did these people serve? This is not easy to answer, but here is the US build up to ‘peak strength’ between 1939 and 1945 according to the National WWII Museum in New Orleans:
Keeping with the theme of ‘peak strength’, here is how each country ranks in terms of number at it’s military peak strength, again according to National WWII Museum in New Orleans:
So that should give you an idea, but remember that these are only estimates and even then they are estimates at peak strength which may be at 1945 or earlier - the museum hasn’t specified dates. So in conclusion, WW2 may be one of the most contentious and written about periods of history, but there is a lot of work to do to understand its scale and logistics. Hope this helps.