There is one important monkey wrench in the above estimates that comes in the episode "Displaced" from Season 3 (E 24). Ironically, the episode is mentioned several times here but not properly vetted for content it seems.
As crew members disappear Janeway establishes two important pieces of a math equation that lead us directly to the proper crew complement:
- crew members are disappearing at a rate 1 crew member every 9 minutes and 20 seconds, or every 560 seconds
- all crew members will be gone in 18 hours
Using these estimates, and with the understanding that there are 64,800 seconds in 18 hours, simple math shows that there are 116 crew members (rounding up even though rounding down would have been more correct, since rounding up favors a higher complement)
I concede to you that Janeway didn't grab a calculator and provide us with hard and fast numbers, so I don't think we should assume these are exact.
While it's tenable that Janeway's estimate should be taken with a grain of salt it should also be believed that, as the ship's captain and someone who is razor sharp at astrophysics and math, it's more or less accurate within an acceptable margin of error.
Most estimates here put the crew count around 146 at the time of the airing of this episode. If that is the case it would be implausible that Janeway would be this incredibly far off in her estimate of time needed for all crew to be replaced, as the necessary time would be over 23 hours, a far cry from her stated estimate of 18.
However, a countervailing monkey wrench is introduced by Chakotey just a few minutes later after Janeway is taken. it is stated at some point that the replacements are 1 to 1, meaning for each Nyran that enters the ship, 1 crew member disappears. When asked for an estimate of crew members left he is told here are 40, and then Chakotay states that more than 100 Nyrans are on board. By this estimate there are at least 141 crew members.
When addressing another episode's probably accuracy, joshbirk stated: "This seems like a good number to take as an accurate count, considering the care that was probably taken in setting up the communication queue."
Originally I agreed with this theory, but having seen this grand contradiction inside of one episode , and that contradiction coming within 4 minutes of the initial estimates from Janeway, I don't believe this anymore.
In the end I think the answer is very simple: The writers never truly and clearly made a final decision as to how many crew members there were.Furthermore, they were clearly careless in their deployment of numbers relating to quantity of crew.
Rather than explain the differences in crew count, they simply assumed no one would be the wiser if they either A) had a hard and fast number that they then played fast and loose with or B) just threw out random numbers in the 115-150 range throughout the series.
I genuinely think this was of not much concern to the writers and they did not take the actual crew count near as serious as us fans have and did not properly anticipate the level of detail to which we would take this in our desire to better understand this part of the ST universe.