There are two questions that do not seem to me to have been clarified for the understanding of a newbie.
1. How do you "deliver" surround sound?
2. How do you "receive" or play back surround sound?
These questions both assume the surround sound has already been created. Let's continue to assume that you have an existing, good, discrete surround sound recording.
Your first question is this: 1.) Do any of the smartphones, mp3 players, etc. have the ability to stream or play a multichannel music file? From what I've found, they only deliver Stereo sound but there MUST be a way (plugin, app) that can do this?
Keep in mind that technically a smart phone in this context is a digital storage device. That is to say, it is capable of holding any digital file - a photo, a document, a spreadsheet, an audio recording - providing the file size does not exceed the capacity of the onboard storage memory. These devices can act as a reproducer of these media: I can see a photo, I can read a document, I can listen to a stereo sound... but they are capable of holding other files that they may not be able to directly reproduce. This is what Otto is referring to when he says "sending signal to stand alone surround sound system." In that case he is using the smart phone like an external hard drive, and playing the surround file through an outboard sound system.
You question seems to be asking if modern digital devices are meant to offer direct outputs to a portable surround listening system. I am not personally aware of such a system. I have received a few promotional emails promoting this product:
http://www.razerzone.com/gaming-audio/razer-tiamat-71
It is designed for so-called "gaming." Has anyone here tried to adapt this to surround music applications? Could the manufacturer be contacted to modify their product? Perhaps a small outboard decoder could interface with the phones via the existing USB connection to decode files????
Fizzywiggs41 is referring to "BINAURAL surround listening," which is still two channel listening which gives some sense of surround effect, such as "Q sound," which was used at least in Roger Waters' Amused To Death and Pink Floyd's The Final Cut. These are still not discrete multichannel listening experiences, which is what I think your question is addressing.
I know of nothing portable other than the product I refer to above. Perhaps you could invent a headband or a hat that would have small external speakers? Could be a fun experiment, and then the sound would not change as you swivel your head. But neither would it be a "private" experience because you would be broadcasting the sound aloud. Maybe a helmet would work - be the life of every party!
Your second question is an encoding/delivery question:
2.) What medium do I have to use in order to get the music to my listeners? I understand that CD is not an option so I assume that I could do a Quadraphonic mix on DVD and/or Blu Ray? Is that true and are those my only options?
There are at least two digital stream delivery options that can encode discrete multichannel music.
1. There is DTS encoding which CAN in fact be recorded onto a normal blank CD disc, but the format is "lossy" like mp3, so many here do not prefer it. DTS also requires extreme caution, because without a decoder it is just digital static, and if it were included in a device set to "shuffle" it could possibly hurt the ears of a listener in headphones. So a DTS recording would want to be stored in a location that was not accessed by the normal stereo player.
2. There are also multichannel FLAC files, which are lossless. I am no expert on these, but certainly they could be played through an app so long as they are delivered to some external playback system of speakers, as discussed above.
3. AAC encoding (particularly HE-AAC) is mentioned above. I don't know about this, but others here do. For all I know this is what is used in FLAC. Someone else can elaborate to enlighten us all.
So as I read your question, the problem with "Modern Day" listening is that you hope to move the surround experience out of the "Olden Day" fixed listening environment of a home multichannel playback system which is not practically transportable. If my assessment is correct, the solution would be the product above or the suggested invention, or some variation of those.