First off, a couple important things to say:
1. I checked around and didn't see any similar builds, if I missed one please let me know.
2. This build started as a joke. I've played hundreds of games with Sona and have always done an AP/CDR build & support items, but was getting bored, so I wanted to build her in a way that would be considered by most people as completely useless, and so far I've won 12/15 games with this build as of the date this is written.
3. This build assumes that you are experienced with Sona and know how all her abilities work, and is NOT recommended for anyone new to Sona. I encourage you to try the "normal" builds first before messing around with this one, seeing as how this build is a lot more dangerous if you don't know what you're doing.
4. You have a slight element of surprise with this build, considering most on the enemy team would probably assume that you have no idea what you're doing by buying these items.

Early Game with this build Sona is very skilled at quickly poking the enemy players, and assuming you're laning with a dps champ, you can probably get off some early kills because you can contribute quite a bit to the overall dmg. You're also able to farm a lot better than an AP/CDR Sona simply because of attacking so quickly, so you're able to get more money faster.

Mid Game, make good use of teleport to help out any lanes that are having some trouble. During this part of the game your ult comes in handy if an enemy player tries to gank you 1v1. You can stun them and generally kill them off instead of just having to run away like normal.

Late Game move as one with your team. Although you put out a pretty good about of dmg, you're still relatively squishy and shouldn't be walking around by yourself.

In terms of your other abilities, make sure to use them wisely as you'll have very little mana regen. Because most of your abilities don't even scale up that well with AP, you're not really letting your team down by not getting much AP, though make sure they know that you heal for less than most Sonas.

In terms of Summoner Spells, I either go Flash/Teleport or Flash/Clairvoyance. I find Teleport helps out a lot more in terms of saving other team members and pushing lanes, but you do unfortunately have to buy more wards than usual if you don't have Clairvoyance. I would never give up Flash, because being a dps champ with this build you tend to stay around the fight more often and most of the time need to get out of there quickly.

I encourage you to try this build a few times before commenting. It's a pretty big change in playstyle if you're used to building Sona in the more traditional way. To those of you that try this build and it doesn't work out, please post what went wrong, what the weak points are, etc etc. And to those of you that try this build and end up liking it, please post your scores with this build.