Probopass : Find a Nosepass and level it up in New Mauville.
Exploud : Evolve Loudred to lv.40. Loudred can be found on Victory Road
Lileep : The only way is by Fossil but I'm sure GTS and Trading Forums will get you one .
Igglybuff : Breed Jigglypuff or Wigllytuff. Jigglypuff can be found on Route 115.
Pichu : Breed Pikachu which can be found in the Safari Zone
Natu : Breed Xatu which can be found in the Safari Zone and Mirage Spots.
Horsea: Route 130, Route 131, Route 132, Route 133, Route 134, by fishing with a Super Rod.
Phanphy : Breed Donphan which can be found in the Safari Zone or Mirage Cave.
Spheal: Shoal Cave as a Wild Pokemon
Marcago : Evolve Slugma which can be found on Fiery Path .
Sealeo : Shoal Cave
Here is a nice list of the Pokemon and their trainer location in the Hoenndex
You do not need Jirachi to complete the Dex