What is the format in which Audio file size will be lowest

Depends what you're trying to encode, and what quality you want... .mp3, .aac (.m4p) and .wma are the standard, of which (in my opinion) .aac gives the best compression to quality ratio.

.ogg/.oga (Vorbis) also give good lossless compression, whilst Sony's Adaptive Transform Acoustic Coding (.aa3) claims to give the same quality at 64 kbps as .mp3 do at 128 kbps.

I've never really used these formats, as when I'm compressing files I want them to be .mp3 so they play on most systems without the need for any extra systems or codecs installed.

If you're trying to get smaller file sizes never save in .wav, .aiff or .au as they are all unompressed file types.

Hope this helps. If you expand your question slightly I'll happily help some more :o)

Ste

To add,
 a simple way to reduce the size
Use a software like super or Audacity  and lower the audio bitrates,
http://www.videohelp.com/tools/SUPER 
basic guide
http://forum.videohelp.com/images/guides/p1608146/basicsuperguide.pdf
http://www.guidesandtutorials.com/audacity-tutorial.html
Here's a brief example
Audio (MP3)
32 kbit/s  MW (AM) quality
96 kbit/s  FM quality
128160 kbit/s  Standard Bitrate quality; difference can sometimes be obvious e.g. bass quality
192 kbit/s  DAB (Digital Audio Broadcasting) quality.
224320 kbit/s  Near CD quality.
Other audio
32-500 kbit/s -- lossy audio as used in Ogg Vorbis
500 kbit/s1 Mbit/s  lossless audio as used in formats such as FLAC, WavPack or Monkey's Audio
1411.2 kbit/s  PCM sound format of Compact Disc Digital Audio
http://en.wikipedia.org/wiki/Bit_rate

Just to comment on Merete's "brief examples". I know someone has posted this somewhere, but you have to look at the rationale of these comparisons: Firstly none of the actual sampling frequencies of 32, 44.1 and 48kHz are mentioned thus negating any comparisons whatsoever. Secondly AM and FM are analogue transmissions, which can transmit any analogue data from speech to badly recorded telephone interviews. When transmitting music, this varied over 4 decades from the transmission of the output of vinyl records, 8 track cassette machines (cart machines) and reel to reel tape to the more recent transmissions of digital data, such as HDD storage material. So how anyone can compare an Mp3 file to an analogue transmission is incomprehensible.
Similarly with digital broadcasting, DAB is the digital radio standard used in the UK, Europe and Australia. In the UK DAB has been reported to be of a lower standard than FM because 98% of UK stations using MPEG-2 audio and a bitrate of 128kb/s. This has recently been updated to DAB+ but still radio stations lower the bitrate to broadcast to a greater number of channels -- so any comparision to DAB is negated.

Re the original question: stehardy88 has actually answered this in asking the author is the question relative to quality, and the author needs to respond if more information is needed, and perhaps to suggest what is trying to be achieved here. Because at the moment the question is like asking what is the most economical form of transport -- so you start with a bicycle and go from there.

And the midi file doesn't qualify as it's a text file not an audio file.

;-)

can I just add, well spoken  BillDL
 that was so cool to read :)

Merete - fredshovel at his best:
https://www.experts-exchange.com/questions/22788158/Need-some-song-titles.html
https://www.experts-exchange.com/questions/20584367/i-want-my-left-speaker-to-be-my-right-and-my-right-to-be-my-left-interchangably.html

Getting back to the question.  Sorry I hijacked it :-(

tauraweb

stehardy88 and fredshovel both gave some very good information, but also asked the very important question about how much quality you are willing to sacrifice in going for the smallest file size.

The end use for the audio files is the important factor, and if you are interested in recommendations most suited to your proposed use for them, then give the experts an idea of how you are going to use the files and you will get some specific recommendations.

Nice trip down memory lane Bill. I'd forgotten that we used to have a bit of fun here.

tauraweb

It appears that you made a mistake in selecting my comment as the "Accepted Solution"?

Bill, she probably prefers walking to bicycles, so it makes sense.

maybe tauraweb liked the idea of using midi as suggested by BillDL  :)

I will await a response, but this isn't right and I'm not really comfortable smiling about it.  My foolish jesting has backfired.  The results have effectively slapped some highly qualified and knowledgeable experts in the face with a stocking full of cold diarrhoea, or a wet fish, whichever sounds the most unpalatable.