As far as I know, it would be impossible to estimate the total number of all people of various races of Middle-earth at any one point in time, especially if you were to include the Hither Lands. Perhaps it would be roughly similar to the population size of mediaeval Europe before the plague.
There are certainly a few more nations and lands in Middle-earth than the ones you mentioned. Mirkwood, Bree, Lothlorien, Dale, Harad and Mordor, to name a few. Do orcs and Nazgul count as "beings"?
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...where the instrument of intelligence is added to brute power and evil will, mankind is powerless in its own defence.
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