Okay... No Dsi. Here is the list of pokemon you are unable to get in heart gold and soul silver:
Assuming you have all the wifi events (which are over and cannot be used) these are the pokemon you can't get. Pokemon Platinum is probably the best choice to get most of these, and it can be found for a cheap price due to the release of generation 5 in Japan.
there are a few pokemon you won't be able to get in either game. So Most of them can be obtained via trading on Wifi. However, since you have to put up a pokemon of your own, you can always breed your pokemon and trade off the eggs. Any starter pokemon, legendaries, and eevee are pretty valuable. The pokmemon Lucario, slamance, and garchomp have high value as well. Pokemon like mew, deoxys, and arceus
that can only be obtained through a nintendo wifi event, aren't required to complete the pokedex. hope this helped a bit!
Also: These pokemon are not required to fill in the pnational dex: Mew, Celebi, Jirachi, Deoxys, Phione, Manaphy, Darkrai, Shaymin & Arceus.