If you do not have a 'Word' tab for your Duolingo Danish course, then either Danish doesn't have one, or you are part of an A/B test and your 'Word' tab is deactivated.
What you can do for a workaround is go to the Duolingo Wiki Userscripts page and install the DuoTweak userscript (follow the instructions under "How to install scripts"). Since the recent rewrite of Duolingo this userscript has unfortunately become almost useless, but it still works on the discussion forum (i.e. click the 'Discussion' tab) and will make the 'Word' tab available to you for any course, even if you are part of an A/B test deactivating your 'Word' tab.
EDIT: So as for the question in the title, "Can I see word strengths when learning Danish with Duolingo?": Yes, using the DuoTweak userscript it is possible (at least for the time being).
EDIT: As of Nov 19th, 2017 DuoTweak and by extension the 'Word' tab still work on the discussion forums (I use them for my Greek course, which has no native 'Word' tab support). To keep the userscript working on my Firefox browser I recently had to change from Greasemonkey to Tampermonkey (these are extensions that enable userscripts) after their change from legacy add-ons to WebExtensions.