Entei and Raiku can be captured through roaming after you see them at the burnt tower. If you follow suicune around Kanto and Johto, It appears at Bills house.
there are many legendary Pokemon in Pokemon heartgold, but the best is HO-OH
I put a link to a guide all about legendary pokemon in HeartGold in the related links.
Trade them from HeartGold and SoulSilver.
In HeartGold you can catch Kyogre.
yes you can also catch them in soul silver.
Articuno
mew
If by enti you mean Entei the legendary dog then yes, all three dogs are there.
I don't think you can refight any legendary Pokemon except the wandering dogs.
migrate and trade
Kyogre is only available for Pokemon: Sapphire on the GBA. Ho-Oh is the legendary pokemon available to you in HeartGold.
No legendary can lay an egg except for manaphy which gives an egg to phione and you can not get manaphy or phione in heartgold