The adoptee is very likely your niece, specifically the half-sibling of the niece you have also tested. The relationship could be diagrammed as follows:
The X-DNA is key to determining this relationship. A useful article to help understand X-DNA matches is X Chromosome Recombination's Impact on DNA Genealogy.
You know that the adoptee is a nearly 100% half match on the X-chromosome with your niece, meaning they share an X-chromosome. A perfect X-DNA match is 196 cM, and she matches at 195.7 cM. By far the most likely scenario for this to occur is that she is the half-sibling of your niece, and that she inherited the same X-chromosome from the common parent (I'm guessing they share a father).
While the conclusions you can draw from the other X-DNA matches are less concrete, it is interesting to note that you share about the same length of X-DNA with your niece as you do with the adoptee. I suspect that you actually share the same X-DNA segments. This would most likely occur because both the niece and adoptee inherited the same X-chromosome from their father (your brother), and no recombination occurred then.
The autosomal matches are consistent with the adoptee being your niece, considering the values given in the Autosomal DNA statistics table. If the above conclusion is correct, the adoptee is:
- your niece (expected to share 1700 cM, actually share 2138 cM)
- first cousin to your son (expected 850 cM, actual 1124 cM)
- half-sister to your other niece (expected 1700 cM, actual 1604 cM)
As you have noticed, you and the adoptee share more than average autosomal DNA for a niece/aunt relationship (thus it is unsurprising that your son has a larger than average match as a first cousin). With autosomal DNA, the average values are just that – there is a wide range of possible values consistent with a given relationship.
Blaine Bettinger has collected data for his Shared cM Project to get a better idea of what the actual ranges of values for a given relationship may be:
According to Bettinger's data, for the relationships above the ranges are:
- Niece/nephew: 1301-2193 (avg 1744 cM)
- First cousin: 533-1379 (avg 869 cM)
- Half-sibling: 1320-2134 (avg 1753 cM)
Your data and the proposed relationships are all consistent with these ranges.
Autosomal DNA inheritance is very much "luck of the draw". The amount of DNA shared, on average, between half-siblings is the same as that shared by an aunt-niece relationship: 25%. The amount a given person inherits is random, which is the main explanation as to why you share more autosomal DNA with the adoptee than her half-sister does. Note that the adoptee and her half-sister share more X-DNA than you do with her however.