There is really no inconsistency. Just slightly different views. Additionally, it seems like the authors in your books use analogies with English which is fine to get a rough idea of how a sound is pronounced but if you want more precision, then you'll have to resort to IPA transcription.
You say,
One books adds that not only when 'A', is stressed should it sound like "AH,"
Here, what you are talking about is the following:
Stressed position: [a] -> [ɑ]
In stressed position, the letter а is usually pronounced [ä] which is the open central unrounded vowel. It sounds kind of like 'a' in the word 'car' or 'father', but unlike it, your tongue shouldn't be retracted to far in the back of your mouth.
там [t̪äm] 'there' (click here to listen)
/a/ is retracted to open back unrounded vowel [ɑ̟] before /l/ as in
палка [ˈpɑ̟ɫkə] 'stick'
[ɑ̟] sounds just like 'a' in the words 'car' or 'father'.
The difference between [ä] and [ɑ̟] bears little significance to Russian speakers. It is just slightly more natural to pronounce them a little differently. So if you can't hear any difference just stick with "father-like" a.
Then you say,
but it should also sound like "AH" when located at the syllable before the stressed syllable. Example - такси (tahk-SEE)
From here, you start to deal with so-called vowel reduction, which consists of two levels.
First level reduction:
In the syllable immediately before the stress (like in 'такси') and in absolute word-initial position, /a/ reduces to near-open central vowel [ɐ] (sometimes also transcribed as [ʌ]), similar to 'u' in the word 'nut'.
паром [pɐˈrom] 'ferry'
Second level reduction:
In all other locations, /a/ is reduced further to a short, poorly enunciated schwa [ə].
облако [ˈobləkə] 'cloud', это [ˈɛt̪ə] 'this' (click to listen)
You go on to say,
while another books has a more expansive definition of "otherwise." It explains that the letter 'A' makes the "Uh" sound when 'A' is in any syllable following the stressed syllable. Another book claims the 'A' makes the "Uh" sound when unstressed and is NOT located in the syllable immediately before the stressed syllable. Another books says 'A' makes the "UH" sound when it is unstressed.
What's going on here is nicely addressed in wikipedia:
In practice, the second reduction has a gradient character: if the vowel in question is afforded enough duration (e.g. due to hyperarticulation), it may be pronounced as [ɐ]. Shorter durations have the effect of gradually transforming [ɐ] into schwa. It has been argued recently that the change of sound quality during second-degree reduction is merely an artifact of duration-dependent "phonetic undershoot", the situation where the speaker intends to pronounce [ɐ], but the limited time budget constrains the likelihood of the tongue being able to arrive at the intended vowel target. During fast speech, reduction ultimately may result in the vowel being dropped altogether, and the preceding consonant slightly lengthened or turned into a syllabic consonant: сапоги [sːpɐˈɡʲi], vs. [səpɐˈɡʲi] ('boots')
And finally, when you say,
Only one book says that 'A' will make a "EE" sound when it is located
after a soft consonant.
You're talking about palatalization. /a/ is pronounced as near-open front unrounded vowel [æ], similar to 'a' in the word 'cat'. (I don't know why your book talks about "ee" instead. This is wrong, at least for stressed syllables).
пять [pʲætʲ] 'five' (listen)
Note that /a/ will be spelled as 'я' to show that the preceding consonant is soft.
When 'я' is reduced in unstressed syllable, it will sound like [ɪ], similar to 'i' in the word 'bit'.
язык [jɪˈzɨk] ('tongue')
