Оплата stands for payment, the act of paying, like in
оплата услуг, so it's governed by question "Оплата чего?", noun + noun in Genitive.
Плата corresponds to the English noun "pay", the noun which is usually explained in dictionaries as "money given in return for work; salary or wages." It's governed by the question "плата за что?".
In colloquial speech those terms quite often are confused and mixed up just like English "payment" and "pay" do.
This is general information. Now, being back to the cases you've mentioned:
- "плата за работу" is correct.
- "получать плату за работу" is correct.
- "получать в качестве платы за работу" or "получать в качестве оплаты работы" are correct.
- "вот плата за работу".
I should mention though that all this cases sounds bit off for Russian speaker. One might say just
вот деньги за работу, "получить расчёт за работу", "в счёт оплаты работы" etc.
UPD: I assume you are from Japan, so here are wiktionary articles on pay and payment in Japanese. Hope this is useful.