Can I sterilize homemade mustard jars in the oven?
What you are doing is not sterilizing the mustard. You just pasteurize it. 

If you just want to pasteurize the mustard: Yes, you can put the jars into the oven instead of water-bathing them. Jars, lids and the content are heated up to 100°C, so it's quite equivalent to water-bathing the jars - if not even better.

Friends of mine put the jars with the lid loose on onto the baking tray with some water (for the moisture in the oven to not to damage the gasket) and then "bake" this for 30-120 minutes (I can't remember how long exactly) at 150-200°C. Then the jars must cool down slowly, therefore the jar must stay for another 30 minutes in the oven which is turned off. I think the lids are closed when the jars are taken out of the oven (but I'm not sure). 
After reading this text 1 I don't know whether to preheat the oven or not. 

Note: In Germany people often can raw food! Since your mustard is not raw, you just need to sterilize the content of the jar and don't need to cook what's inside. Therefore the cooking/baking  time should be decreased. 

If you want to sterilize your mustard, you need weck jars with rubber seals and steel tension clips. When baking the jars with the contents and the lid on, secured with a rubber seal and the tension clips at more than 120°C, the contents are sterilized like in a pressure cooker. The rubber seal and the tension clip act as a valve. After baking, the contents are vacuum-sealed. See wikipedia article about home canning. 


image by Alupus.



1


  Das Wasser darf nur langsam erhitzt werden. [...] Je nachdem, wie weich das Einweckgut ist, dauert das Einkochen zwischen 10 und 120 Minuten. Danach dürfen die Gläser wiederum nur sehr langsam abkühlen. [...]
  Statt auf dem Herd kann man auch im Backofen einkochen. Zum Einkochen im Backofen die Fettpfanne mit Wasser füllen, auf die unterste Schiene schieben und die Einweckgläser, wie oben beschrieben vorbereitet, hineinstellen. Obst bei 150 bis 160 Grad einkochen, Gemüse bei 190 bis 200 Grad. Die Gläser danach noch 30 Minuten im Ofen stehen lassen und anschließend zugedeckt abkühlen lassen. 


translated freely:

[The first paragraph deals with canning with a water bath] The water must be heated slowly. [...] Depending on how soft the food the be canned is, the canning takes 10 to 120 minutes. After that the jars must cool down very slowly.[...]
Instead of canning on the stove you can also do this in the oven. Put the jars onto the baking tray and pour some water into the tray. Fruits are canned at 150°C to 160°C, vegetables at 190°C to 200°C. After that, the jars stay another 30 minutes in the oven [note: which is tuned off] and afterwards let these cool down covered up.