Which effects/technics to use on poorly recorded audio in Audition CC

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You might try posting your thead to an Adobe Audition forum.  There might be a few people here who are familiar with the software, but you'll probably get more info there.
 
My guess, without hearing the audio is that you will need to eliminate noise (I believe there is a noise reduction plug-in in Audition) and then increase the gain on the signal.

Audio restoration, clarifying, cleaning up etc. is really a job where what you do and the order you do it depends on the problems the audio in question has. Every time is different, and sometimes the best results you can get still aren't ideal. Without hearing the original audio in its original, uncompressed (either as an mp3 or following any audio dynamic compression such as youtube adds to everything) raw state it's almost impossible to suggest what to do.

You're probably best asking for help in an Audition or audio restoration forum as has been suggested.

Sameple audio. Change "xx" to ""tt". Perhaps this will work. And thank you everyone for all the useful information.

hxxps://www.dropbox.com/s/jd7dnsw3geac9ph/recorded_audio.mp3?dl=0

 Thank you for the link. I am not where I can upload or post at the moment, but will circle back on this later on.
 
Just to clarify, I have Adobe Audition (AA) 4.0, which came with Creative Suite 5.5. Some of the menu items may be different, but I believe these are all identical. I will walk through the steps on that particular file so you can replicate it as needed.
 
If you save while working, save it as a wav file, so you do not compound errors when using a lossy format. You may also want to work in smaller chunks for this (CPU and RAM capability will be important for the 1+ GB wav I used)... the biggest thing is the noise reduction part (Step 2 below).
 
So for this file:
Step 1: Favorites -> Normalize to -3 dB - This will normalize the volume of the track (including noise).
 
Step 2: Noise removal -

1. Zoom into the file where only noise is visible. For this I used the noise area from 27:16-27:18.
2. Drag select that region. Select Effect -> Noise Reduction / Restoration -> Capture Noise Print (Shift-P). Acknowledge the pop up.
3. Click on the track anywhere to remove the selection area. This is required so you remove the noise from the entire track, not just the selection.
4. Select Effect -> Noise Reduction / Restoration -> Noise Reduction Process (Ctrl-Shift-P). Leave the default settings alone, click Apply.

Step 3: EQ the track. An aggressive HP filter at around 100 Hz, and aggressive LP filter at about 5K will pass only voice similar to a telephone. The included plugins with AA are not the greatest, so chose ReaEQ (which is a free plugin, not knowing what you have). This requires more description for you, but is basically to pass the core of the voice, and reduce everything else.
 
Step 4: Compression. iZotope has a multi-band compressor (Effects->Amplitude and Compression->Multiband compressor), but none of the presets are great. This is to reduce the "pumping effect" and further reduce the sound outside of the vocal range. The bigger part that is hard to tame in the track once heading down this path is the natural room reverb, so certain sections are fine without this.

Quick update - I ran through this again a couple more times, and the best way to attack this is to do it in sizeable chunks so your computer can handle the load. Also realize that AA has heal, denoise functions I did not use.
 
I took the 20-25 minute segment and saved it as a 32-bit wav file, then did the following:
 
Step 1 from above.
Step 2 from above, using the noise from roughly the 21 minute mark (original file), or 1 minute mark in the extract.
Step 3 I simply ran the De-esser (there are 3 inside AA that I have, but this is the one on the Favorites->De-esser which is an automatic function (no popups)).
Step 4 Rather than use an EQ this pass, I used TDR Kotelnikov (free compressor*) using the preset of "Vocal Bus Tight." There are still some artifacts from using this, but not egregious.
Step 5 Ran Effect->Stereo Imagery->Center Channel Extractor
Step 6 Raised the output gain of the track by 3dB
 
Offloaded roughly 21:10-24:20 (original file), which was 1:10-4:40 in the extract, converted to a 160Kbps mp3 which I posted here. Let me know if/when you want me to pull that file down. [Edit: File deleted per post #13 below.]
 
*Not sure how familiar you are with adding VSTs to AA, but once installed, is via the Effects->Audio Plugin Manager...
 
There is more that can be done with that file, but it will never get to "perfect" status. I was trying to get the easiest path for you to work it to an acceptable level.

That multiband is nice, but not a one size fits all and can easily generate artifacts. It is the best built-in next step for the plosives and evening the track segments.

iZotope apparently makes some plugins integrate with AA (as menu items). I hit one effect to see what it was and it popped off Neutron and ran an automated routine with no insight as to what it was doing... Just said "Processing Neutron" and done. After I saw that I began wondering if that multiband is a stock AA plugin or from an iZotope plugin I purchased.

Done.
 
Not sure if you are familiar with the use of compressors. Jeff Evans posted an excellent "How to" a while back that you may find useful as you move forward with things. Due to the variations of that track, working with segments that are similar is the best way to attack it.
 
AA's "Auto Heal" tool is something that is useful for rogue transients, and I have found most useful using the sonogram/spectral view. If you span a transient, so that the tool can see "good info" on either side (using the select tool to create a box), it has the best chances of performing well.