No, Smy isn't dislodged because AEG cuts Con's support. I'm pretty sure the dislodgement of the fleet doesn't change anything.

Ok thanks diplomat.

The only time a dislodgement stops a tap is if the tap is directed at the support dislodging the unit. A unit can't cut support directed at itself.

"A unit can't cut support directed at itself."
It can, but only if it doesn't get dislodged by it. Though that would imply dislodging the support rather than simply cutting it.

Actually, what happens if:
Turkey:
A Bul-Rum
F Bla S Bul-Rum
Austria:
A Ser-Rum
A Bud S Ser-Rum
Russia:
Rum-Bud

Would the support from Budapest be cut and Turkey dislodges Rumania? Or would The two supported armies simply bounce in Rumania? Because Rumania is not dislodged by the support from Budapest, is it able to cut it, allowing Turkey to enter Rumania?

I believe Turkey and Austria will bounce, and Russia will stay in Rum. Rum can't the cut support of an attack upon itself. Thus the battle between Austria and Turkey is 2 versus 2, which means neither succeeds.

This is what the rules state:
Support is cut if the unit giving support is attacked from any province except the one where support is being given.

This means Rum can't cut Bud's support. The situation is the same as if Rum had simply been ordered to hold.

Ok so in a nutshell a nudge given by unit x to unit y remains effective, even if unit x is dislodged by units a and b?

@dD_ST - The rules clearly state a unit can not cut support directed against itself. Irregardless of if it gets dislodged. There fore, in the second example Turkey and Austria bounce because Russia can'rt cut support directed against itself. Period. No exceptions about unless it is dislodged by the support. Sorry, you are wrong there.

Yes.
Going back to your original question: Even if Dislodged, Aeg can still cut Con's support of Smy, as the rule state:
 "A unit being dislodged by one province can still cut  support in another province. Just as a unit being dislodged   by one province can still cause a standoff in another, a unit   still manages to cut support even if it's dislodged. Just make   sure that the dislodgment isn't coming from the province   where the unit is giving support. (Remember this rule: A   dislodged unit, even with support, has no effect on the   province that dislodged it.)"