Christians have addressed this in various ways:
Some (a very small minority), such as Marcion challenged premise 1. - they didn't believe in the Old Testament. Most Christians have rejected this approach to the extent of labelling those who adopt it as being heretical.
A slightly bigger group (comprising the likes of Seventh Day Adventists and Messianic Jews) would take serious issue with your premise 2. - they take the Old Testament law seriously and do seek to follow whatever part of it that can still be followed (considering that the destruction of the temple has practically put paid to all the laws related to temple worship, Orthodox Jews are in the much the same boat here).
The vast majority of Christians would challenge your premise 3. as being a completely false characterization of what Jesus did and taught:
17 “Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19 Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 20 For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven. - Matthew 5:17-20 NIV
Additionally, many would make the point that although God is Lord over all, the Mosaic law wasn't given to humanity in general, but to the children of Israel in particular, and the vast majority of Christians are not descendants of Israel, but gentiles - they are, by default, excluded from the Mosaic Covenant therefore they are not bound by it's provisions. Of more relevance are the commands given to Noah from whom all are believed to be descended and these provisions were actually reiterated by the early Christian Church at her first general council.
Your point 4. is completely moot - the Old Testament has not (except by Marcion and his ilk) been disavowed and there is therefore no direction to follow "other Gods".