DONT USE 9V (RECTANGLE) BATTERIES!..
they are notoriously CRAP!!!!
And yes.. the Arduino has a +5 RAIL.... but can only supply (max/maybe) 40mA of current of any given pin... your servo will need more than that, especially under load..
and when we say external power source, you can still use one battery pack to power everything.. but you connect it directly to the battery pack.. not through the Arduino..
Battery Pack A >>> Arduino
Battery Pack A >>> servo(s)
Battery Pack A >>> led strip
NOT...
Battery Pack A >>> Arduino >> Servo >> leds
keep in mind.. EACH of these require specific and different voltages (so regulate appropriately)
I dont do "FB"...
and any help should be posted here for everyone to benefit from... (although all your answers are here already, posted several times)
edit-
I see memebr beat me to it! lol..