Every person is to be in subjection to the governing authorities. For there is no authority except from God, and those which exist are established by God.

2 Therefore whoever resists authority has opposed the ordinance of God; and they who have opposed will receive condemnation...(Romans 13:1-2)

My question is that should we obey laws of government, if they oppose the Biblical teachings - like if government legitimize abortion, allows same sex marriage, allows universalism, allows mercy killings, do we have to obey them because Paul tells us that if we disagree, we disagree with God and will be condemned?

I am little confused here, how can we obey what is against God and His commandments? Any thoughts?

Nearly in all the countries of the world, murder is not allowed, so is rape, stealing things from others is not allowed and many such laws that coming directly from the Ten Commandments. In Many countries, where Christianity is not followed, those Laws are acceptable that does not make a believer in sin. Therefore, as Paul said, we need to respect authorities and live in peace. He did not tell us to live in sin but he said to live in peace.

However, some countries allow, living with partners, but many don't live an unholy life. Some boast of their tattoos yet many live a Christian life without tattoos. If a rule is passed where abortion is legalized, so a Christian always have an option, not to follow it. If same sex marriage is allowed, then people who do not fear God will get into this contract, yet some will live happily as Christians.

Therefore, I do not find any connection or relevance of the question to the verse you have mentioned. You always have an option to live a holy life. I simply do not find it confusing.

However, God has told us in the Bible, not to take the "Mark of the Beast". It means, that we are not to follow any Law that will put us to death. Moreover, lust is sin, having illicit relations with a man or woman is not allowed. So basically, we say "no" to many things that are happening around us.

Conclusion

Paul asked people not to rebel against the authorities and try to take over the authorities with power. Our power does not lie in weapons, suicide bombers and intrigues. Our power comes from Almighty God from whose word everything was created. Paul never said something contrary to Bible;

Keep your tongue from evil
and your lips from speaking lies
Turn from evil and do good;
seek peace and pursue it (Psalms 34:13)

God has made it very clear in the Bible, we are not to follow evil, whether we are attracted to it or forced to it.