See in my there is a lots of difference between two exclamations one difference is that in the first exclamation I feel very close in relation with God because using pronoun my. But in another exclamation I am feeling that there are many another and I am one of the others who are in close relation with God.
The first exclamation makes feel better and more positive and great feeling of devinity. But the second making me to feel less positive and not giving as much satisfaction as the first one.
See in my view it is very better to remember god in your own way which satisfy you and God also satisfied by you.
It is better to pray for another including you then praying for your own.
So while remembering god remember him as your single and while praying or wishing or asking pray like there are many other who needs their wishes get true including you.
To use it as a phrase and an exclamation is considered sacrilegious and against the tenets of Christianity, because we do not take God's name in vain. It is one of the Ten Commandments. "Thou shall not take thy God's name in vain". So, swearing by God or taking His name as an exclamation is incorrect. Most literary works also, use goodness or gosh, instead of God. Very rarely have I come across the phrase as described by you, being used by native speakers of the language or those who are proficient in it.
The phrase if used is done to beseech God or in prayer - not to show our astonishment. Some people do use it and the phrase probably has its roots in Christianity, as we often reflect in prayer and say, My Lord and My God.
My God, because He is my God and I am praying or looking at Him for succour.
"A love affair with knowledge will never end in heartbreak" - Michael Garrett Marino
So in our exclamation we utter 'oh my God' rather saying ' oh our God'.
This particular exclaimation is very popular in society and whenever we feel that something has happened which should not have happened then this exclaimation comes out involuntarily.
Even the atheist the non believers in God use it frequently and do not understand that by saying this they indirectly agreeing to His presence or existance.
Thoughts exchanged is knowledge gained.
But pray God for everybody.
But for many individuals it may appear more natural to take as Oh My God. Even in many languages we exclaim with the words equivalent of My Go. So it will be just normal and natural to take OMG as Oh, My God!.
But many prayer songs and verses have the collective plural denoting we ,our or us in them.It is only when we atone for our wrong doings and ask for pardon that we use the first person singular as I , me or my.
'Idhuvum Kadandhu Pogum "
Even this challenging situation would ease
I have seen people saying " My God is a good God - My God is a powerful God - My God is moving ahead of me - My God only can save me - My God never fails - and much more to add about their God.
No life without Sun
So not only religion but there exists many gods for each community and caste and unless and until the mind set of people changed to god is one and he existed every where and for which again God has to prove like Narasimha Avatar. That reminds me when I visited a locally popular Swamiji who always says even God appears before us we may not believe and ask for his ID card(Now may be aadhaar card).
OMG we may not take it as Oh my God it will only be Oh My Goodness.
Nice to be in ISC and feel the difference.
A small doubt. If OMG is 'Oh My Goodness' used to wonder something good, Can we use OMB "Oh My Badness" to wonder something bad?
No life without Sun