4 More saved bytes!

# Python 2 535 517 473473468 bytes

I'm pretty sure this can get golfed further, so I'll keep tryingSaved 5 bytes thanks to make it better.@Easterly Ink!

n,l,t=input()
b=[7,3,1,5,0,4,2,6][:n]
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for'for _ in[1]*w] forin[1]*w]for _ in[1]*h];a=j%2;b=[(k+1)%8 for%8for k in b];print ''b];print''
if a:g[Y][X:X+2]='/\\';g[Y+1][X:X+2]='\\/'
else:g[Y][X+1]='_';g[Y+1][X:X+3]='|_|'
for k in b:k=k+8*a;x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X;y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y;exec"g[y][x]='|/_\\\\'[k%4];x+=d[k%8];y+=d[(k-2)%8];"*l
for k in z(h):print ''print''.join(g[k])


# Python 2 535 517473 bytes

I'm pretty sure this can get golfed further, so I'll keep trying to make it better.

n,l,t=input()
b=[7,3,1,5,0,4,2,6][:n]
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for _ in[1]*w] for _ in[1]*h];a=j%2;b=[(k+1)%8 for k in b];print ''
if a:g[Y][X:X+2]='/\\';g[Y+1][X:X+2]='\\/'
else:g[Y][X+1]='_';g[Y+1][X:X+3]='|_|'
for k in b:k=k+8*a;x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X;y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y;exec"g[y][x]='|/_\\\\'[k%4];x+=d[k%8];y+=d[(k-2)%8];"*l
for k in z(h):print ''.join(g[k])


# Python 2 535 517 473468 bytes

Saved 5 bytes thanks to @Easterly Ink!

n,l,t=input()
b=[7,3,1,5,0,4,2,6][:n]
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' 'for _ in[1]*w]for _ in[1]*h];a=j%2;b=[(k+1)%8for k in b];print''
if a:g[Y][X:X+2]='/\\';g[Y+1][X:X+2]='\\/'
else:g[Y][X+1]='_';g[Y+1][X:X+3]='|_|'
for k in b:k=k+8*a;x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X;y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y;exec"g[y][x]='|/_\\\\'[k%4];x+=d[k%8];y+=d[(k-2)%8];"*l
for k in z(h):print''.join(g[k])

3 Woohoo! Just save a bunch of bytes through rearranging/further golfing!

# Python 2 535 517517473 bytes

n,l,t=input()
b = [0,4,2b=[7,63,1,5,30,7][4,2,6][:n]
r=1,
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for _ in r*w]in[1]*w] for _ in[1]*h];a=j%2;b=[(k+1)%8 for k in r*h]
b];print a=j%2''
if a:
g[Y][X:X+2]='/\\'
g[Y+1][X\\';g[Y+1][X:X+2]='\\/'
else:
g[Y][X+1]='_'
g[Y+1][Xg[Y][X+1]='_';g[Y+1][X:X+3]='|_|'
for k in b:
k=k+8*a;
x=[0k=k+8*a;x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X
y=[01][k]+X;y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y
for _ in r*l:
g[y][x]='|0][k]+Y;exec"g[y][x]='|/_\\'[k%4]
x+=d[k%8]
y+=d[_\\\\'[k%4];x+=d[k%8];y+=d[(k-2)%8]
b=[(a+1)%8 for a in b]%8];"*l
for k in z(h):
print ''.join(g[k])
print ''


# Python 2 535517 bytes

n,l,t=input()
b = [0,4,2,6,1,5,3,7][:n]
r=1,
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for _ in r*w] for _ in r*h]
a=j%2
if a:
g[Y][X:X+2]='/\\'
g[Y+1][X:X+2]='\\/'
else:
g[Y][X+1]='_'
g[Y+1][X:X+3]='|_|'
for k in b:
k=k+8*a;
x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X
y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y
for _ in r*l:
g[y][x]='|/_\\'[k%4]
x+=d[k%8]
y+=d[(k-2)%8]
b=[(a+1)%8 for a in b]
for k in z(h):
print ''.join(g[k])
print ''


# Python 2 535 517473 bytes

n,l,t=input()
b=[7,3,1,5,0,4,2,6][:n]
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for _ in[1]*w] for _ in[1]*h];a=j%2;b=[(k+1)%8 for k in b];print ''
if a:g[Y][X:X+2]='/\\';g[Y+1][X:X+2]='\\/'
else:g[Y][X+1]='_';g[Y+1][X:X+3]='|_|'
for k in b:k=k+8*a;x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X;y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y;exec"g[y][x]='|/_\\\\'[k%4];x+=d[k%8];y+=d[(k-2)%8];"*l
for k in z(h):print ''.join(g[k])

2 deleted 112 characters in body

# Python 2 535535 517 bytes

n,l,t=input()
b = [0,4,2,6,1,5,3,7][:n]
r=1,
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for _ in r*w] for _ in r*h]
a=j%2
if a:
g[Y][X:X+2]='/\\'
g[Y+1][X:X+2]='\\/'
else:
g[Y][X+1]='_'
g[Y+1][X:X+3]='|_|'
for k in b:
k=k+8*a;
x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X
y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y
u=d[k%8]
v=d[(k-2)%8]
s='|/_\\'[k%4]
for _ in r*l:
g[y][x]=sg[y][x]='|/_\\'[k%4]
x+=ux+=d[k%8]
y+=vy+=d[(k-2)%8]
b=[(a+1)%8 for a in b]
for k in z(h):
print ''.join(g[k])
print ''


# Python 2 535 bytes

n,l,t=input()
b = [0,4,2,6,1,5,3,7][:n]
r=1,
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for _ in r*w] for _ in r*h]
a=j%2
if a:
g[Y][X:X+2]='/\\'
g[Y+1][X:X+2]='\\/'
else:
g[Y][X+1]='_'
g[Y+1][X:X+3]='|_|'
for k in b:
k=k+8*a;
x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X
y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y
u=d[k%8]
v=d[(k-2)%8]
s='|/_\\'[k%4]
for _ in r*l:
g[y][x]=s
x+=u
y+=v
b=[(a+1)%8 for a in b]
for k in z(h):
print ''.join(g[k])
print ''


# Python 2 535 517 bytes

n,l,t=input()
b = [0,4,2,6,1,5,3,7][:n]
r=1,
w=5+2*l
h=w-3
X=w/2
Y=h/2-1
z=range
d=[0,1,1,1,0,-1,-1,-1]
for j in z(t+1):
g=[[' ' for _ in r*w] for _ in r*h]
a=j%2
if a:
g[Y][X:X+2]='/\\'
g[Y+1][X:X+2]='\\/'
else:
g[Y][X+1]='_'
g[Y+1][X:X+3]='|_|'
for k in b:
k=k+8*a;
x=[0,2,3,3,2,0,-1,-1,0,1,2,2,1,0,-2,-1][k]+X
y=[0,0,0,2,2,2,1,0,-1,-1,0,1,2,2,0,0][k]+Y
for _ in r*l:
g[y][x]='|/_\\'[k%4]
x+=d[k%8]
y+=d[(k-2)%8]
b=[(a+1)%8 for a in b]
for k in z(h):
print ''.join(g[k])
print ''

1