How would you decline this noun? It can not be 1st, 2nd, or 3rd declension. Also, how would you say "of Aeneas", which is genitive case?
It is of the first declension, but not of the most typical kind.
I would divide the first declension into four classes:
NOM -a -ās -ē -ēs ACC -am -am/-ān -ēn -ēn GEN -ae -ae -ēs -ae DAT -ae -ae -ae -ae ABL -ā -ā -ē -ē VOC -a -ā -ē -ē
The last three classes are reserved (almost completely) for Greek names. The first class is by far the most common one, and it is typically the only thing mentioned in introductory material.
When the nominative ends in an -s, the name is a masculine. The ones ending in -a and -ē are feminines, although there are exceptions in the biggest class.
The name Aeneas is declined as in the table above. The genitive is Aeneae. Incidentally, the Latin form of my name (Ionas) is declined in the same way.