Here are some options for developing online quizzes that are public and can then be embedded into a page.
Polldaddy's interface is straightforward and allows image and video embeds either in the question stem or in the choices (if you're using multiple choice questions). It handles correct/incorrect answers, but doesn't allow branching (based on which choice a quiz-taker selects) so if you want to give your quiz-takers any feedback between each question, you can insert a page of text.
Google forms do offer branching based on a quiz-taker's choice. Google forms do not allow you to attach media to each multiple choice item but you can insert media just above a multiple choice question,
With Quizlet the emphasis is memorising terms - it lets you make a list of terms and definitions (with image or voice for each definition) and then present them to your viewers in different ways e.g. flashcard, matching items, or drag & drop game. However, there is no feedback on responses.
Testmoz was developed by an undergraduate student at the University of Vancouver and does not require you to create an account. You need to know HTML to images or other media which are already hosted elsewhere (and which you are permitted to use in this way) by typing HTML into the question field when setting up the quiz (n.b. it doesn't work well with Flickr iframe embeds for example). It’s hosted, free, and tracks responses (exportable to CSV). However, there is no feedback on responses.
Easy to setup and can be embedded on other webpages. A downside is the results page show a lot of other random quizzes.