The phylogeny of Y-DNA haplogroup J has changed over time. Is your J2a4 defined by the L26/S57 mutation ?
J2a4 has 8 known subclades, with many more sub-subclades. You probably belong to one of them, but I can't help you much without knowing which it is.
For example, J2a4a (M47) is found mostly in the northern half of the Middle East, in Iran, Iraq and Turkey, but J2a4b (M67) is most common around the Caucasus, and also widespread in Anatolia, Greece, Italy and southern Iberia.
MtDNA haplogroup K almost certainly originated in the Near East. There are so many subclades that it is hard to say where it came from. A HVR1+2 test is not sufficient to known which subclade of K1a you belong to. But the full sequence test is still quite expensive and won't help you a lot now.
K1a itself might also have originated in the Near East, but that could be anywhere between the Caucasus and the Levant.
At present it is impossible to say if it is associated with the Indo-Europeans, the early Neolithic farmers, the ancient Greeks, the Phoenicians, or several of them. Considering the wide spread of K1a in North-West Europe as well as the Middle-East, I would rather see the early Neolithic farmers from Anatolia and Greece as the main population source.