1.申し訳ありません
2. ごめんなさい
3.申し訳ない
4.ごめん
I WOULD SAY
storonger 1 > 2 > 3 > 4 > weaker
It's not a poker game(black-spadess are storonger than red-hearts) but I would say 申し訳ございません is the strongest apology in these 4, and ごめん is the weakest.
Also I think there is a particular rule of using them.
- 申し訳xxxxx is formal. it's more used in a public situation.
If you apologize to your boss, use this one.
- ごめんxxxx is more used in a daily/cusual situation.
When you apologize to your girl firend, you would use this type of apology.
Again,
申し訳xxx = for your boss, customer, girl firend's parents or other public situation
ごめんxxx = for your friends, pairents(most of the time), girl firend, or any cusual situation
わりぃ・悪い=for your firends, extremely(too) cusual, better use it only to your very close friends. or better not use it.
Also "すみません" could be substituted to "申し訳xxx", but "すみません" is even weaker than "申し訳xxxx".
So if you hear someone says "申し訳ありません” to you, the person is apologizing you really deeply.