ShakeyX, I think you took my IPA advice way too seriously. If you can't really see any substantial difference between [ɛ] and [е], - OK, that's the point: just use the sound from "red". Russians have only one conceptual "Eh"-like sound, which is realised slightly differenty depending on surrounding sounds.

It would be another story if you were to generate synthesized speech. In that case playing the EXACT sound from лес in the word весь would lead to a somewhat unnatural result for an ear trained to hear normal Russian. If you insist, sound example for [ɛ] demonstrates a "generic" Э i.e. if you were to ask me how "э" sounds in Russian, I would say it whis way.

As for the soft/hard vowels, calling them so is a convention in some books. In reality, Russians tend to only differentiate between six vowel sounds: А, И, У, Э, О, Ы. Now, there are soft and hard variations for consonants. OK, consonants before И always become soft, and consonants before Ы always remain hard. What about numerous words where consonants become soft before А or, say, Э? You have a choice: either introduce 14 more consonant letters - or reuse vowels, which are smaller in number (or use Ь each time, which would be a disaster for Russian). Russian takes latter approach. 4 more symbols for vowels are introduced: Я = йа/ьа, Ю = йу/ью, Е = йэ/ьэ and Ё=йо/ьо.*** If such a vowel letter is word-initial or comes right after some other vowel, it starts with Й (яблоко ~ /йаблака/). Otherwise it just softens previous consonant**** (unless a consonant doesn't have a soft counterpart, like Ж/Ш/Ц) like this: ветер ~ /в'эт'ир/. И is a naturally softening vowel, its "hard" counterpart is Ы (which sounds pretty different).
*** I have written Э=йэ/ьэ and so this way just for sake of clarity. In actual Russian orthography soft sign + vowel means BOTH softening a consonant AND adding Й. For example: бульон = /бул'йон/
**** In many foreign borrowings Е stands for Э and doesn't soften previous consonant: термос /`тэрмас/, экзодерма /экза`дэрма/, интернет /интэр`нэт/. As you can see, it is mostly for dentals (Т/Д/Н).