Perl, 99 characters
@P=map{$/.substr$".'__/ \\'x99,$_,$W||=1+3*pop}0,(3,6)x pop;
chop$P[0-$W%2];print" __"x($W/6),@P
Last edit: Saved one character replacing -($W%2) with 0-$W%2 (thanks A. Rex)
Explanation:
For width W and height H, the output is 2+2 * H lines long and 3 * W+1 characters wide, with a lot of repetition in the middle of the output.
For convenience, we let $W be 3 * W + 1, the width of the output in characters.
The top line consists of the pattern " __", repeated W/2 == $W/6 times.
The even numbered lines consist of the repeating pattern "\__/ ", truncated to $W characters. The second line of output is a special case, where the first character of the second line should be a space instead of a \.
The odd numbered lines consist of the repeating pattern "/ \__", truncated to $W characters.
We construct a string: " " . "__/ \" x 99. Note that the beginning of this string is the desired output for the second line. This line starting at position 3 is the desired output for the odd lines, and starting at position 6 for the even numbered lines.
The LIST argument to the map call begins with 0 and is followed by H repetitions of (3,6). The map call creates a list of the substrings that begin at the appropriate positions and are $W = 3 * W + 1 characters long.
There is one more adjustment to make before printing the results. If W is odd, then there is an extra character on the second line ($P[0]) that needs to be chopped off. If W is even, then there is an extra character on the bottom line ($P[-1]) to chop.