In a furious troubleshooting spree I found a workaround, which may not be the optimal way to do things, but it worked for me:
=SUMIFS(Intäkter!H5:H105; Intäkter!A5:A105; ">2013-09-30"; Intäkter!A5:A105; "<2013-11-01"; Intäkter!D5
105; "=Översättning SVE-ENG")
I removed the "equal or greater" and "equal or less" with "greater" or "lesser", and moved the dates to the last of the previous month, and the first of the following month. And then I could add my 3rd criteria that checked the type of service and it all worked flawlessly. Such a relief
In case someone has similar issues I thought I'd let the thread be and add this, instead of editing and removing the original post.