Python 2, 123 112 110 109 100 98 bytes

i=n=input()
while i:a=i%2;print' '*(n-i)+'\%s/'%['_',((-~i/2)*'/   \  |'[a::2])[a:-1-a]][i>1];i-=1

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Saved a bunch of bytes by using input and string formatting as in Rod's answer

Python 2, 123 112 110 109 100 98 96 bytes

i=n=input()
while i:a=i%2;print' '*(n-i)+'\%s/'%['_',((-~i/2)*'/   \  |'[a::2])[a:~a]][i>1];i-=1

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• Saved a bunch of bytes by using input and string formatting as in Rod's answer
• Saved 2 bytes thanks to Mr. Xcoder

Python 2, 123 112 110 109 bytes

n=input()
for i in range(n):a=(n-i)%2;print' '*i+'\\'+['_',((~(n-i)/-2)*'/   \  |'[a::2])[a:-1-a]][i<n-1]+'/'

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Python 2, 123 112 110 109 100 98 bytes

i=n=input()
while i:a=i%2;print' '*(n-i)+'\%s/'%['_',((-~i/2)*'/   \  |'[a::2])[a:-1-a]][i>1];i-=1

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Saved a bunch of bytes by using input and string formatting as in Rod's answer

Python 2, 123 112 110 bytes

def f(n):
 for i in range(n):a=(n-i)%2;print' '*i+'\\'+['_',('/   \  |'[a::2]*(a+(n-i)/2))[a:-1-a]][i<n-1]+'/'

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Python 2, 123 112 110 109 bytes

n=input()
for i in range(n):a=(n-i)%2;print' '*i+'\\'+['_',((~(n-i)/-2)*'/   \  |'[a::2])[a:-1-a]][i<n-1]+'/'

Try it online!