I read sometimes pdf's written in Finnish. I was unable to search text containing letters ä and ö by Xpdf and Okular. Is there a PDF-reader which finds those letters correctly? I had a problem with the file elisanet.fi/matti.t.lehtinen/Geom2011.pdf.
I am using Evince and have to read German every once in a while. Evince correctly finds ö and ä (and other German special characters like ß).
I do have special keyboard shortcuts for those characters (using the right meta key), but you can also copy and paste them in the search field if your keyboard cannot produce them.
One thing to keep in mind though is that it is possible to create a PDF where the output looks like ä, however the graphic being composed of separate 'ä' and '¨' (a separate diaeresis/umlaut). In that case you will not find it by searching the accented character. So try out finding just 'a' and 'o' on the actual PDFs before switching your viewer.
If you look at the file with
pdfedit then for the highlighted segment (sorry it is a bit small, it is on page 2 of the document):
the encoding is in an array like this:
As you can see there is little connection between the diaeresis and the 'o' (from the first field), the offsets place it there and that is not a "simple" UTF16 to UTF-8 or other character encoding conversion that you can automate.
If the text didn't have so much math in it you could try rendering to image and then do OCR, but in this case I think you better try and contact the author and get the original (probably LaTeX) source if you need to search in the text.