Reverse Greek Conversion Golf

Python 3, 112

Saved 4 bytes thanks to vaultah.

Booyah, beating JS!

lambda x,z="ΑΒΓΔΕϜΖΗΘΙΚΛΜΝΞΟΠϘΡΣΤΥΦΧΨΩϠ".find:sum((z(c)%9+1)*10**(z(c)//9)for c in x)

With test cases:

assert(f("ΡΚΓ")==123)
assert(f("Η")==8)
assert(f("ΨΟΖ")==777)
assert(f("Ρ")==100)
assert(f("ΧϜ")==606)

Loops through the string and uses its index in the list of potentials chars to calculate how much it's worth.

JavaScript (ES7), 115 bytes

s=>[...s].map(c=>n+=((i="ΑΒΓΔΕϜΖΗΘΙΚΛΜΝΞΟΠϘΡΣΤΥΦΧΨΩϠ".search(c))%9+1)*10**(i/9|0),n=0)|n

Haskell, 116 113 bytes

f x=sum[v|d<-x,(l,v)<-zip"ΑΒΓΔΕϜΖΗΘΙΚΛΜΝΞΟΠϘΡΣΤΥΦΧΨΩϠ"$(*)<$>[1,10,100]<*>[1..9],d==l]

Usage example: map f ["ΡΚΓ","Η","ΨΟΖ","Ρ","ΧϜ","ΡϘ","ΜΒ","Ν"] -> [123,8,777,100,606,190,42,50].

Lookup the value of the greek letter from a list of pairs (letter, value) and sum. The list of values is build by (*)<$>[1,10,100]<*>[1..9], where (*)<$>[1,10,100] builds a list of functions [(*1),(*10),(*100)] (multiply by 1, 10 and 100) which are applied separately to the elements of [1..9] and concatenated into a single list.

Edit: 3 bytes with thanks to @xnor.