Convert Complex Chinese Numbers into Arabic Numbers
05AB1E, 52 51 bytes

0•9∊»£¬ƵçoiKβÐg•19вIÇƵª%èvX¨UOy¬iθ°UX‰¤_ªX*]DgiX*}O


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0                              # literal 0
 •9∊»£¬ƵçoiKβÐg•19в            # compressed list [2, 14, 0, 3, 0, 8, 0, 6, 2, 9, 0, 18, 0, 1, 0, 13, 5, 0, 10, 0, 0, 7, 12, 4]
                   IÇ          # codepoints of the input
                     Ƶª%       # modulo 270
                        è      # index into the above list, with wraparound
v                 ]            # for each number y in that list:
 X                             #  push the variable X
  ¨                            #  drop the last digit
   U                           #  store that in X
    O                          #  sum all numbers on the stack
     y                         #  push y
      ¬i          ]            #  if the first digit of y is 1:
        θ°                     #   10**(the last digit of y)
          U                    #   store that in X
           X‰                  #   divmod X
             ¤_ª               #   if the modulo is 0, append 1
                X*             #   multiply by X
Dgi  }                         # if length of the top of stack is 1:
   X*                          #  multiply it by X
      O                        # sum of the stack
                               # implicit output