Not sure I followed everything you wrote.
14ga is plenty for a remote turn-on (assuming that you're using it to only switch items on and not power anything).
Remote turn-on leads should already be fused from the Headunit.
Always use RMS ratings, max numbers can be highly exaggerated and lead to the wrong size fuse.
Do the amps already have fuses? If not, their manuals should state what to fuse them at.
Amps aren't 100% efficient so they will input more power then they output. Therefore you have to take that into consideration when fusing.
Do you have a multimeter that can measure current? You could use that to measure how much current the LED strips are pulling.
Depending on how many you're running, LEDs use very little current so without knowing what you have, a 5a fuse is probably fine.
Where is this relay sourcing its power from? A distribution block in the trunk or a seperate power wire from the battery?
This is strictly for the turn on all of my power wire is fused correctly. I just needed to know if I need to fuse the turn on lead from the junction box to the amp turn on's. I am running the relay from the 12v wire that would power my head unit so power is only there when I am actually using the radio. So lets clear this up I need to turn on my 3 amps, power 8 led strips and not have my car electricals go crazy in the process. I order the relay, junction box and 14 gauge fuse holders. Now What?