The Russian expressions in the title refer to god. Are there equivalent interjections that do not refer to it?
The list contains right expressions but by no means it is a complete one. You often would also hear "С ума сойти!", and bizarrely enough, some totally inexplicable exclamations referring to the same emotion of awe or astonishment like, for example, "япона мать!".
Keep in mind that the majority of such expressions are from the realm of profanity and cannot be mentioned here. But believe me - once you are in Russia, you would learn them very quickly.
Maybe, if you don't want to allude the God, you wouldn't want to call the devil either. :) Or, at least, to use swearing words.
Let's discuss what you can use in a decent society.
So, you can call your mother, I mean the exclamations:
Just as here, when Piglet saw his balloon burst, he shouted: "Мама, мамочка!"
Мать моя женщина! is also possible, but only in informal conversations.
Historically, it was (and is) possible to call your father (and the other respected men of your community) as well. :)
If you are most likely to call all people in general to help you, you can exhale:
Люди добрые! (Что делается!)
Also, you can name the situation what it is like, if it is really bad, then it will be:
If you are happy, on the contrary, you can say:
If you are astonished, you exclaim:
С ума сойти!
С ума сойти можно!
Ого!, Ух ты!, Ничего себе!, Надо же!, Вот это да! go here as well
Mind that "с ума сойти" is more stylistically neutral, while обалдеть and рехнуться are colloquial.
But, still, we do use "Боже упаси!", "Господи, помилуй!", "Боже сохрани!", "Бог миловал!", "Слава Богу!". It was funny, when I was interpreting for a judaic organization and heard "Христом Богом тебя молю!" there. :) Because the Russian language and culture are firmly connected with christianity, and even our letters were invented by christians and spread over the orthodox part of the world.
During the Soviet times, when any religion was prohibited, there were certain trials to replace such expressions in literature. E.g., in "Мойдодыр" by Чуковский there is the following place:
Боже, Боже! Что случилось?
Отчего же всё кругом
И помчалось кувырком?
In most editions this innocent phrase was replaced by
Что такое, что случилось?
But even at that time, and we can trace it as we watch the films shot in different decades, people still used the God-calling expressions. And they also could use the devil-calling expressions (чёрт побери, да чёрт бы его побрал, где тебя черти носят?, чёрт его знает, чертовщина какая-то, чёрти что, etc.), and get the answer "Не чертыхайся!" or "Не ругайся!", which meant 'don't swear'.
It has always been better to say "Да Бог его знает!" (I don't know), "Иди с Богом!", "Бог знает что" instead of "Да чёрт его знает!", "Иди к чёрту!", "Чёрт знает что". Those phrases are not totally synonimous, but even if you mean the second part, you can mitigate your message using the first part.
Sure, there exists one swearing expression to express all the "мамочки!", "ужас!", "люди добрые!" and "красота-то какая!", but it's not what I would like to share here or to hear from a foreigner. ))))))