The only things left to consider before Apple repair are USB audio and Bluetooth audio. I got a Syba "usb audio card", which is a little dongle that goes in the USB port and supplies headphone & microphone jacks, off Amazon for $8 shipped, and it's been great. Well, except it is a bit wide and blocks the adjacent port, so I also got a 6-inch usb cable off eBay for $4 shipped. Probably for more $$ you could get a Bluetooth audio reciever or headset, and ditch the connection entirely. Good luck.
The Apple 3.5mm headphone jack may have multiple different failure modes, since it contains 4 equally flimsy electrical contacts. Staring into the glowing red Cylon eye, they are: 2 "sleeve" contacts (nearest you), one at 9 o'clock and one at 3 o'clock (positions on an imaginary 12-hour analog clock dial); 1 "ring" contact (farther in) at 12 o'clock; and 1 "tip" contact (all the way in) also at 3 o'clock. The one plaguing my Late 2006 MacBook is the tip contact. Tugging on it with a bent-tipped safety pin while watching through a magnifying glass works, but only until the next time I unplug the headphones, and so is too impractical. Jostling it with things like air, suction, Q-Tips, toothpicks, ballpoint pen inserts works for some, but not for me. What works for me 100% of the time is inserting a 1/8" metal rod all the way and then dragging it out while applying moderate pressure in the 9 o'clock direction (towards the MagSafe connector). There is no problem using metal, even powered on, because headphone...