What does using your onboard soundcard (which I really wouldn't recommend) have to do with whether or not you can use JBL speakers? 

MME is the old (very old) Microsoft standard for game cards.  Latency will most likely be horrible if you record or edit. 
 
If your drums sound better through a $5 game card into speakers rather than headphones it is likely you have a problem in the mix stage.  The point of mixing is to have a file that transfers between systems and sounds good on all of them.  Unless you are going to buy your exact system for anyone who wants to listen to your music way you intended it.
 
Hang in there - there is a lot to learn about basics.

Sanderxpander
What does using your onboard soundcard (which I really wouldn't recommend) have to do with whether or not you can use JBL speakers? 

I just need the right cables from the 6MM Mono jack in the AKAI to a mini jack. Should be possible, I was just under the impression that my headphone was the way to go.

AT
MME is the old (very old) Microsoft standard for game cards.  Latency will most likely be horrible if you record or edit. 
 
If your drums sound better through a $5 game card into speakers rather than headphones it is likely you have a problem in the mix stage.  The point of mixing is to have a file that transfers between systems and sounds good on all of them.  Unless you are going to buy your exact system for anyone who wants to listen to your music way you intended it.
 
Hang in there - there is a lot to learn about basics.

I know this. I was just testing this with playback only and it works ok for this. I also setup an Airplay connection to my speakers in the living room and it IS already better. Not perfect, but I'm on the right track.

Zargg71
The JBL (LSR) 305 has gotten a lot of positive feedback since they came out. I think you will be very happy with them. 
All the best

+1 on LSR 305's, got them when they first came out, great monitors for the price!

One more thing that I figured would be mentioned by now (or maybe I missed it) is if you are stuck using headphones most of the time (like I am) and/or cannot afford proper monitors just yet you may want to look into a device by Focusrite called the "VRM Box".
 
It's basically a little device with bundled software that emulates different monitors, soundsystems and environments through your headphones. There is a "Pro" studio environment with common pro monitor emulations, a "Living Room" environment with different stereo system emus and a flatscreen TV emu. And there's a "Bedroom" environment with some of the smaller pro and consumer emus as well as computer speakers and whatnot.
 
It's not perfect of course and doesn't replace a properly treated room and/or proper monitors but it does provide a bunch of alternative and reasonably accurate sound sources and common listening environments. I've have been getting much better mix results since I started using it to comb through all the settings and finding bad spots in miy mixes. I combine that with my pure headphone sound, my monitors (which are good but in a bad room and I can't crank them) and all the other sound sources I have like a bunch of consumer headphones, two stereo systems and whatnot.
 
Bonus is that it acts as an audio interface too if you need it to. No inputs and just the stereo headphone out but it's perfect for just writing MIDI, editing or mixing through. It's super small and uses USB for power and audio when it's being used as the main interface so it's portable.
 
It's also got a big, slick and smooth volume knob on it so it can be used as a "Big Knob" for volume if nothing else (you can hook it up as a kind of a slave to your main interface via SPDIF... in fact that's how I use it). A good studio volume control costs almost or as much as one of these things (about $100).
 
Anyway, I don't work for Focusrite. Just very happy I bought this thing. It's been immensely useful and sounds like it could be just what you need while you sort out all the other suggestions made here.
 
Cheers and good luck.

Beepster
One more thing that I figured would be mentioned by now (or maybe I missed it) is if you are stuck using headphones most of the time (like I am) and/or cannot afford proper monitors just yet you may want to look into a device by Focusrite called the "VRM Box".
 
It's basically a little device with bundled software that emulates different monitors, soundsystems and environments through your headphones. There is a "Pro" studio environment with common pro monitor emulations, a "Living Room" environment with different stereo system emus and a flatscreen TV emu. And there's a "Bedroom" environment with some of the smaller pro and consumer emus as well as computer speakers and whatnot.
 
It's not perfect of course and doesn't replace a properly treated room and/or proper monitors but it does provide a bunch of alternative and reasonably accurate sound sources and common listening environments. I've have been getting much better mix results since I started using it to comb through all the settings and finding bad spots in miy mixes. I combine that with my pure headphone sound, my monitors (which are good but in a bad room and I can't crank them) and all the other sound sources I have like a bunch of consumer headphones, two stereo systems and whatnot.
 
Bonus is that it acts as an audio interface too if you need it to. No inputs and just the stereo headphone out but it's perfect for just writing MIDI, editing or mixing through. It's super small and uses USB for power and audio when it's being used as the main interface so it's portable.
 
It's also got a big, slick and smooth volume knob on it so it can be used as a "Big Knob" for volume if nothing else (you can hook it up as a kind of a slave to your main interface via SPDIF... in fact that's how I use it). A good studio volume control costs almost or as much as one of these things (about $100).
 
Anyway, I don't work for Focusrite. Just very happy I bought this thing. It's been immensely useful and sounds like it could be just what you need while you sort out all the other suggestions made here.
 
Cheers and good luck.

Thanks for the info. There's also Monitorizer available in Pro and Plat, but I don't know if it's any good.

Listening to the tracks and also LOOKING at the wave forms I think your suffering from not so much the recording part, but mixing and mastering. Your songs are a little out of balance and the overall level is weak. 
LOOK at a commercial recording of that style of music and you will see the waveform is a solid brickwall. There's no room for dynamics in pop music. ( and even country now) Slam that puppy with your mastering tools and get your average RMS level around -12db. My guess is your 10db away from that goal. 
 
Oh, and on the topic of vintage synths, I was making a track for Mony Mony and wanted a Jump kinda sound I must have spent way to long looking. I had to preview most all the soft synths that looked possible.  I was shocked at how bad a lot of the included stuff was, what is all that for??  Anyhow I finally found it in Roland Groove synth. Synth Stack. And even funnier was a great patch in  Good old TTS-1! Just crank the chorus up. 
Which brings up another point, if you want good synth sounds, you need to go beyond the pre sets and start editing. It's always been that way. 

Oops... yeah I was going to mention the Monitorizer thingie too.
 
I haven't actually tried it yet (been doing more sessions than actual hardcore mixing) but definitely it's another option and ALL options are good when it comes to reference sounds.
 
Really though, from what I've read, it's no where near the level of options the VRM Box gives. It actually strikes me as more of a tool for more in depth tests of wiring configs and mono stuff as opposed to actual room and speaker emus.
 
I should give the bugger a poke to see what it's all about first hand.
 
Cheers.

Hey, garbage in: garbage out. You didn't even spell your thread title correctly so it's worth pointing out good music is made by people who sweat the details...on every kind of setup imaginable. Keep trying!