Idomeneo is scored as follows:

Woodwind
piccolo
2 flutes
2 oboes
2 clarinets (in A and in B/B flat)
2 bassoons

Brass
4 horns (in D, in C, in B flat (alto)/in B (hoch), in G)
2 trumpets in D
3 trombones

Percussion
timpani in D and in A

Strings
Violins I & II
Violas
Cellos
Basses

Continuo in recitatives
Harpsichord or violoncello

The score of the opera can be viewed online here with a larger, scrollable version available here

Idomeneo
Re di Creta ossia Ilia a Idamante
Synopsis of Plot - Composition - Orchestration - Roles - Noted Arias