Applescript : text delimitation in a loop
An XML file can’t have identical keys at the same level, so I’m going to guess that it is just a plain text file with those entries.
Text item delimiters can be used for everything, but it would tend to add a bit more code, since you would need to get a list of items using the first delimiters, then use additional delimiters on those items, and so on.  In this case, you can use them to just break the text apart at the desired key, then get the text from between the first set of tags by getting their offsets, for example:

property keyValue : "&lt;key&gt;myValueTime&lt;/key&gt;"
property startTag : "&lt;string&gt;"
property stopTag : "&lt;/string&gt;"

set theSource to "&lt;key&gt;myValueTime&lt;/key&gt;        &lt;string&gt;2019-03-28T08:48:18+0000&lt;/string&gt;
&lt;key&gt;serviceToken&lt;/key&gt;
&lt;key&gt;myValueTime&lt;/key&gt;
  &lt;string&gt;2019-03-29T09:48:18+0000&lt;/string&gt;
&lt;key&gt;serviceToken&lt;/key&gt;
  &lt;string&gt;whatever&lt;/string&gt;"

set saveTID to text item delimiters
set text item delimiters to keyValue
set classValues to text items of theSource
set text item delimiters to saveTID

set myCaseNotes to {}
repeat with anItem in classValues
  set here to (offset of startTag in anItem)
  set there to (offset of stopTag in anItem)
  if here is not 0 and there is not 0 then
    set the end of myCaseNotes to text (here + (count startTag)) thru (there - 1) of anItem
  end if
end repeat

return myCaseNotes