Well, your question is very good and the answer is NO! You cannot use all three forms interchangeably because they have different meanings. I am sorry I do not know the third form in your question, and although I spoke a lot of Japanese, I never encountered a situation where such an expression was necessary (but this is my experience).
That being said, I would like to consider your question and provide a wider answer by explaining the forms that I know in Japanese to express when some action is performed or occurs before another one.
Using (V:て-Form)から〜 expression
Usually this is the first expression taught when learning Japanese Grammar. It is the one used the most because it is really versatile and quite easy (although it requires knowledge of the て-Form which is not always mastered in the early days of Japanese lessons). The pattern is the following (please note punctuation):
(V:て-Form)から、(...Sentence)
Here are some examples:
1a) 毎{まい}日{にち}シャワーを[浴]{あ}びてから、朝{あさ}ご[飯]{はん}を[食]{た}べている。
=> Everyday after taking a shower, I have breakfast.
2a) 昨日{きのう}は[洋]{ヒロ}[子]{コ}ちゃんと[遊]{あそ}んでから、帰{かえ}った。
=> Yesterday after playing together with Hiroko, I returned home.
3a) 明日{あした}はちょっと[忙]{いそが}しいんだよ。学{がっ}校{こう}をでてから、すぐアルバイトに[行]{い}かないと！
=> Tomorrow is quite busy. After leaving school, I must go to my part-time job.
You use this form every time you want to describe an action which takes place after another one. The sentence using the て-Form is the one whose action happens first. After a comma, you then specify what happens next.
Using (V:た-Form)あとで〜 expression
You use the following pattern whenever you want to specify that a certain action has been completed and then you moved on:
(V:た-Form)あとで、(...Sentence)
Consider the following examples:
1b) 宿{しゅく}題{だい}をしたあとで、遊{あそ}んでもいいよ。
=> After you finish homework, you can play and have fun!
2b) 小{しょう}説{せつ}を[書]{か}いたあとで、立{た}ちあがって「やった」と[言]{い}ったんだ。
=> After writing the novel, he stood up and said "Done!".
3b) クラスが[終]{お}わったあとで、友{とも}達{だち}と[遊]{あそ}びに[行]{い}った。
=> After classes finished, he went playing somewhere with friends.
As you can see, here are situations where a certain activity has been completed, performed, or finished once and for all. When you want to express this concept, you should use this form. Sometimes it might be incorrect to not use it.
Also please note that you should use あとで and not 後で. This is a grammar rule in Japanese that my teachers always told me (since I had a bad habit of using kanji everywhere): in grammar patterns, you should use hiragana, not kanji.
Using (V:辞-Form)と〜 expression
Another expression to express sequential situations is the following:
(V:辞-Form)と、(...Sentence)
You use the jisho form (base form) in order to say that after a certain thing happens, then inevitably, the next sentence occurs. I have chosen these terms (happens and occurs) not by chance. Consider the following examples:
1c) 右{みぎ}へ[曲]{ま}がると、パン[屋]{や}が[左]{ひだり}側{がわ}にあります。
=> Once you turn right, there will be a bakery on the left.
2c) ８時{じ}３０分{ぷん}になると、クラスが[始]{はじ}まる。
=> When it is 8:30, classes will start.
3c) 二{は}十{た}歳{ち}になると、何{なん}でも[出]{で}来{き}るようになるよ。
=> Once you turn 20, you can do anything.
In this situation, the sentence should always be translated as following:
(V:辞-Form)と、(...Sentence)
==> (Sentence-1)と、(Sentence-2)
==> Once (Sentence-1) then (Sentence-2)
It is important to point out that this pattern should be used when giving directions and when describing actions, matters, or situations. The grammar rule actually use the word inevitable in order to describe when to use this structure. So when some actions is performed or some event occurs, it is inevitable that a consequence occurs as well. This connection cause-consequence is depicted perfectly by this grammar structure.
Conclusion
As you can see, there are several options. I described the ones I know and that I think are the most used. As you can see, you cannot interchange these patterns. Hope it helps.
