Hidden Power Calculator

Ruby, 210

a=$*.map.with_index{|a,i|[a.to_i%2<<i,a.to_i[1]<<i]}.transpose.map{|a|a.inject &:+}
$><<"#{%w(Fighting
Flying
Poison
Ground
Rock
Bug
Ghost
Steel
Fire
Water
Grass
Electric
Psychic
Ice
Dragon
Dark)[a[0]*15/63]} #{a[1]*40/63+30}"

First time golfing, so I guess this is pretty obvious solution.

CJam, 140 115 bytes

q~]W%_1f&2bF*63/"GMÿD>BÙl½}YÛöí6P¶;óKs¯¿/·dǯã®Å[YÑÌÞ%HJ9¹G4Àv"256b25b'af+'j/=(euooSo2f/1f&2b40*63/30+

Note that the code contains unprintable characters.

Try it online in the CJam interpreter: Chrome | Firefox

Pyth, 110 bytes

J+dGA.b/*iN2CY63Cm_+0jd2_Q"("r@cs@LJjC"!�W��Zm�����A�zB0i��ȏ\"���?wC�ǀ�-#ך
?ЫܦO@�J/m���#"26)G3+30H

This contains unprintable chars. So here's a hexdump:

00000000: 4a 2b 64 47 41 2e 62 2f 2a 69 4e 32 43 59 36 33  J+dGA.b/*iN2CY63
00000010: 43 6d 5f 2b 30 6a 64 32 5f 51 22 0f 28 22 72 40  Cm_+0jd2_Q".("r@
00000020: 63 73 40 4c 4a 6a 43 22 10 21 de 57 ad c8 5a 1c  cs@LJjC".!.W..Z.
00000030: 10 6d e0 d6 12 f6 80 bc 41 85 7a 42 30 69 ae 80  .m......A.zB0i..
00000040: c8 8f 5c 22 a0 84 ab 3f 77 43 01 ca c7 80 d0 1d  ..\"...?wC......
00000050: 2d 23 d7 9a 0a 3f d0 ab dc a6 4f 40 b9 4a 2f 6d  -#[email protected]/m
00000060: d2 ca c6 23 22 32 36 29 47 33 2b 33 30 48        ...#"26)G3+30H

You can also download the file pokemon.pyth and run it with python3 pyth.py pokemon.pyth

The input 30, 31, 31, 31, 30, 31 prints

Grass
70

Explanation:

J+dGA.b/*iN2CY63Cm_+0jd2_Q".("
J+dG                            store the string " abc...xyz" in J
                 m      _Q      map each number d in reverse(input list) to:
                     jd2          convert d to base 2
                   +0             add a zero (list must have >= 2 items)
                  _               reverse the list
                C               zip
                          ".("  string with the ascii values 15 and 40
     .b                         map each N of ^^ and Y of ^ to:
         iN2                       convert N from base 2 to base 10
        *   CY                     multiply with the ascii value of Y
       /      63                   and divide by 63
    A                           G, H = ^

r@cs@LJjC"longstring"26)G3+30H
        C"longstring"           interpret the string as bytes and convert 
                                from base 256 to base 10
       j             26         convert to base 26
   s@LJ                         lookup their value in J and create a string
                                this gives "fighting flying ... dark"
  c                    )        split by spaces
 @                      G       take the Gth element
r                        3      make the first letter upper-case and print
                          +30H  print 30 + H