What does the word 'mandles' mean?

Solution 1:

The OED gives it as an archaic form of "mandil," "mantel" and "mantle." Mandil is obsolete; the other two are in current use. http://findwords.info/term/mandle

"Mandel" is German for "an almond nut", which might explain the "mandles in the trees" and also "a tonsil" which seems less plausible for your animal reference. Maybe "mandibles" is the modern word there. http://dictionary.reverso.net/german-english/Mandel%20%5BNuss%20mit%20Schale%5D

"Mandl's paint" was a treatment for tonsillitis. http://drpaulose.com/general/587

For "Mandlen" and chicken soup, see http://www.oxforddictionaries.com/definition/english/mandlen

The "liveray mandles" ("livery", i.e. part of a uniform?} sold by the dozen are presumably "mantles" of some kind.

Solution 2:

In reference to your first block quote, about "soup mandles", here is a pertinent article from Wikipedia:

Shkedei marak (Hebrew: שקדי מרק‎, literally soup almonds), known as mandlach in Yiddish, or as "soup mandels" in the United States, is an Israeli food product consisting of crisp mini croutons used as a soup accompaniment. Shkedei marak are small yellow squares made from flour and palm oil. As a parve product, they can be used in either meat or cream soups. Despite the name, they contain no almonds.

Although it is a reference to an item of traditional Ashkenazi Jewish cooking, and as such, is fairly obscure, it is based on a Yiddish word meaning almond, and most likely refers to the item's shape.

It is a real word, as opposed to the "man-candles" concept.