They only differ in pronunciation of consonant,
and not in vowel sound afer it.
OMG! Vox! Are you okay?
1. Try saying "Нина" and if you can imagine Ы instead of И then.....hmmm....I missed something in my life.
2. Cut the first consonant in the "мяч" out using audacity or something and try to hear the A there.....
3. Try to hear the O while saying "Сёмга".
4. Try to hear the У while saying мюсли/кюре/пюре.

Thinking this way will cause learners to aforesaid mistakes, that's why I repeat to treat them as pairs:
If they treat the Я as the A but soften the consonant properly, they will get the М'AСО instead of МЯСО, which is the most common mistake.
Then they hear that something's wrong and start adding the Y-part to get the Я correct and that causes another mistake.
I'll record the 1-st one:
http://www.sendspace.com/file/596phk
Do you see what happened when I tried to preserve the A original without softening? It's exactly the same thing I talked above of, referread as an accent.

The reason of you can hear the hard sounds is because of stretching them.
If you stretch sounds like мяяяяяяяясо you will hear the A because of the tongue moving to the "hard" position in these longer things. But when said normally these sounds sound really soft. The softness appears at the connection of the soft consonant and the soft vowel and lasts about 1/4 of a second, because it's not a convenient position for the tongue in vowels, it starts moving into the convenient resting position (which corresponds to the hard pair of the vowel), or to the position needed for the next sound intended to be said.

if you knew German that would be easier to explain, but Russian soft vowels with the Y-part cut off sound very close to the umlaut-things in German (double dots above).
They are also front ones and they are also soft ones.

If you listen to the recording attentively starting from different positions of the МЯУ word, you will notice how the soft M is turning into the SOFT A (Я) and only then, just right before the У, it's being turned into the hard A, because we need to say the У, but not the Ю, and lowering the middle of the tongue immediately affects the Я turning it into the A.

Dissecting sounds this way like a surgeon, you can guess now why you won't hear the hard vowels instead of the soft ones in the entirely-soft-words like няня, дядя etc., because it's not needed to move the middle of the tongue into the hard position and nothing affects the soft vowel bothering you to hear it.