Syllables and mora

I have recently discovered the linguistic term 'mora' as a subset of a syllable and am thinking through some examples.

How would the word 'stretched' be analysed? Is it one syllable? And what are its mora?

As John Lawler notes in the comments, morae are not inherently interesting in English and there is no common method for determining the morae for a given English word. This makes answering your question prohibitively opinionated.

Kris' comments supply a little more perspective:

In English, the codas of stressed syllables represent a mora (thus, the word cat is bimoraic), but for unstressed syllables it is not clear whether the codas do so (the second syllable of the word rabbit might be monomoraic). — Wikipedia

Although some authors advocate the mora in English (e.g., Hayes, 1989; Pierrehumbert & Nair, 1995), others recognize the tremendous difference between the putative mora in English and the mora in "true" mora languages such as Japanese (e.g., Kubozono, 1990; Beckman, 1995). — Structure in Language: A Dynamic Perspective

In the end, I recommend you try it out for yourself and then ask for opinions in EL&U chat.

To actually answer your question, however, "stretched" is considered one syllable and could be broken into various sub-syllables. I have personally heard people pronounce the word stre-tched or str-etche-d depending on their infliction, dialect and mood. You could presumably use this as a starting point for determining the morae.

It has the exact same number of morae as 'strength' :-)

You asked for an answer, not for suggestions, so here's mine: There are four morae in each of these words.

s-tre-tch-ed [s-tre-tsh-t]

s-tre-ng-th [s-tri-ngk-th]

The exact breakdown of which sound belongs to which mora is open for interpretation.

The word "stretched" is one syllable.

In general, syllable onsets are not considered to contribute to mora count (there are some possible exceptions, but they are rare and controversial; see "Moraic Onsets" by Nina Topintzi for an overview). So we can ignore the "str".

A phonologically "short" vowel is one mora long. Generally, "stretched" would be considered to have a "short" vowel, so that gets us up to one mora.

Then, as the Wikipedia quote of MrHen's answer says, the presence of a coda consonant /tʃ/ would generally be considered to get us up to two morae.

The word-final consonant /t/ can be analyzed in various ways. One somewhat common analysis of English final inflectional consonants like this is to treat them as extrametrical; in that case, it would not contribute to the mora count and we would only have two morae overall.

If we use an analysis without the concept of extrametricality, it might be analyzed as adding another mora, although I'm not really familiar with this kind of analysis.