You may first wish to begin by consulting a parallel Bible or a more modern translation. It is important to update the grammar of the Bible periodically lest important meaning be lost in words that fall out of the collective English vocabulary or (and perhaps worse) meaning appear where there was none as meanings and language evolves and changes.
Furthermore, modern translations are origional translations which are able to pull from thousands of origional sources that we did not have centuries ago and have several hundred more years of scholarship to benefit from. In contrast, the American Standard Version of the Bible is a revision of the King James Version of the Bible which is itself a revision of the Bishops' Bible (which also had 1 revision under the same name) which was a translation made in the 1500s at the request of the Church of England. Basically, this is the translational equivelant of the Telephone Game.
In looking at more modern translations and using a Parallel Bible, you will first notice that most translations now translate Colossians 2:9
For in him all the fullness of deity lives in bodily form
This distinction is important because the ASV makes it sound like Father, Son and Holy Ghost (the entire Godhead - 3 in 1) are crammed into the body of Jesus like sausage stuffed into a casing. In other translations, it becomes clear that Colossians 2:9 is simply saying that Jesus is fully deity - that is fully God - incarnate in a human body. This means that it is only the Son which is incarnate. Not Father and Holy Ghost also.
This translational distinction is also important because only people are indwelt with the Holy Spirit (note the use of the word "dwell" in 1 Cor 3:16), while only Jesus is deity incarnate and these two things are different. The dictionary defines being incarnate as being "embodied in flesh". Indwell on the other hand means to inhabit. Thus it is the difference between dwelling in a house and being a house. The ASV just does not capture this nuance.
Furthermore, as other answers have noted, the Holy Spirit dwells alongside our spirit and (to expand) we already have a bodily form. Our souls have already been incarnated as a body which is also a difference between Christ's incarnation and our indwelling. Additionally, while Jesus is incarnate deity this by nature makes him God. When we are indwelt with the Holy Spirit however, we do not share in the deity of God and remain merely human.
Finally, for Christians we are only filled with the Holy Spirit, while Jesus was the Son; distinct from the Holy Spirit and we are not indwelt with Jesus. We can only indwelt with Jesus the son vis-à-vis the Holy Spirit. I think you will find that when the Bible speaks of indwelling the believer, it is only with the Holy Spirit.
As an aside, though Ephesians 3:19 uses the phrase "fullness of God" it should be noted that this does not refer to God the father (or the son,) but the Holy Spirit. The Holy Spirit was represented by Water (See John 7:37-44 and Genesis 1:2). Thus to be "filled up" evokes the imagry of being filled with water like a jug and is a clear reference to the Holy Spirit - the same imagry that nearly caused Jesus to be stoned in John 7 for claiming to be God.