Jim and I are of age. This means that you are old enough to satisfy some legal criterion (old enough to drive, to sign contracts, to drink alcohol, etc.)
Jim and I are of "the age". I would expect this to be punctuated as shown, and would be an informal and somewhat sardonic expression. This means that you are at an age when characteristics of older people appear, such as frailty, which you and Jim are bearing wearily.
Jim and I are of an age. This is much less common, and could refer to you and Jim belonging to a particular era. It could also be part of a longer statement, "Jim and I are of an age where we should know better," meaning you're old enough to know better.