Yes it can. I use it quite often. Usually in situations where I want to be a little amusing, perhaps. Example situation: my friend's husband arrives home with a huge bunch of flowers, and a very guilty look upon his face. He has probably done something wrong. So, I turn to my friend and say, "Methinks your boyfriend is going to be sleeping on the sofa tonight!" What I mean is, even the flowers won't help him. He's done something very bad, and my friend won't be pleased with him. So the sofa it will be! That's the sort of situation where I might say methinks.

Er... sorry... I changed her husband into a boyfriend half way through my last answer. Methinks I am very stupid sometimes!

I am a German, but I love to use methinks from time to time with my English friends. I usually say it, when I told them a long and elaborate theory of mine and there is this awkward silence afterwards...always a good moment to add a quick "methinks". Not sure, it is the right use, but it worked so far...methinks. :D

I agree with the above answers. I don't really think it's ironic, it is used more for fun. I like hearing it used like that from time to time : )

It's only ever used in a jokey, mock-Shakespearean tone.