More or less all variants are used in one context or another.
In historical, biblical or arabic contexts, the usual construction would be:
Pippin, Sohn des Karls
Isaak, Sohn des Abrahams
which can, of course, be affixed to an I am:
Ich bin der Sohn des Karls.
(But that sounds very weird; this type of construction is really only used to introduce or address someone very important.)
Ich bin Sohn des Karls.
is possible, if there is something important (or you feel that there should be some implication) attached to the opposite side knowing who’s son you are.
Ich bin Sohn des Kaisers!
Auch Majestäten zahlen Eintritt.
In a less formal/historical or whatnot setting, it is often shortened in the way you suggested with postfixed genitive:
Ich bin der Sohn Karls.
It is also possible to use the standard prefixed genitive albeit without the definite article.
Ich bin Karls Sohn
These two may lead to the difficulty in differentiating between Andrea and Andreas. But honestly, if your father is Andreas or either of your parents are Andrea, you will just avoid this specific construction altogether. And actually, you wouldn’t use it in colloquial speech anyway (genitive is rather rare in colloquial German). In written form, the presence (Andreas’) or absence (Andreas) of an apostrophe clearly indicates the person’s name.
In colloquial speech — at least to me, implying South Germany — it is perfectly fine to use the von construction. However, note that in my area an article with the name is mandatory, leading us to:
Ich bin der Sohn vom Karl.
Which can also be turned around:
Ich bin vom Karl der Sohn.
And then there is a multitude of versions you may here but never read and which always succeed at irritating northerners, such as:
Ich bin dem Karl sein Sohn.
Note: never ever ever use that in your German class or write it.