Will I get audio and video from my MacBook on TV by connecting mini DVI to DVI adaptor to DVI to HDMI cable then to HDMI input on back of Sony SXRD TV. I was told I could use the mini display to DVI adaptor but that did not work.
MiniDisplayport didn't work because your computer has a Mini-DVI connector(if your first part was correct), not a MiniDisplayport (plastic pre-unibody=Mini-DVI, Unibody=MiniDisplayport).
You won't get audio in either situation though, as both MiniDVI and the MacBook's MiniDisplayport only carry video. You'll need a separate audio input (headphone jack to RCA most likely) to carry the audio.
Will I get audio and video from my MacBook on TV by connecting mini DVI to DVI adaptor to DVI to HDMI cable then to HDMI input on back of Sony SXRD TV. I was told I could use the mini display to DVI adaptor but that did not work.
I don't know if you have a miniDVI or miniDisplayPort output, as you didn't tell us more about your hardware, but both outputs don't support transfer of audio signals (in short: no sound), so you need an extra cable or two.
Have a look at this extensive guide, which could have been found by search: