I've done a lot of things simultaneously. 'Weirdest' is an interesting and interpretable adjective, plus the way the question is worded, it may be that the weird part is about the two things individually, and not the 'weird' quotient when the two things are done at the same time.
Top Ten Things I've Done Simultaneously - Weird Edition
10) Drinking water while peeing. Water goes in, water goes out. The circle of life, through my trap and peehole. The Trap and Peehole is also the name of my family's oldey time tavern.
9) Having sexual relations while considering whether or not I should answer the phone. Maybe to you, consideration isn't a 'thing' because there's no action involved. But in this particular case, it's substantial to be going through the process of who it might be and if you want to talk to that person while inside another person. (For those who still think this shouldn't count, I did answer the phone. So I was fucking while talking, so there.)
8) Burping and farting. This one's a classic, but it don't make it any less weird. Kinda feels like everyone gets a taste when you let this fly.
7) Getting an erection while having no interest in sex. Again, 'having no interest' may not be an action, but it sure fucking feels like a tangible hindrance when someone wants your bonestuff and you'd rather eat pizza. But I can't say no to boobs, so I gotta push through.
6) Making a phone call while on the toilet. Another one that everyone does and no one admits too. This was invented thirty seconds after the portable phone was invented. "You'll never guess where I'm calling you from. Plop."
5) Giving oral sex while receiving oral sex. I've talked about this on-blog before. Simultaneous mouth buggering (SMB or 69) only works when both people are of the same skill level. Otherwise, one starts to lose focus and stops doing a good job on the bits in their face, and then it becomes awkward position single mouth buggering (AP-SMB or 84).
4) Reading and Sleeping. You might deem that this is normal, but think about it. You know your body wants to go to sleep, but you're fucking determined to get to the end of the chapter, no matter how little information you're actually taking in. Then, you end up having to go back and read over the shit the next day. And you know this. And you try anyway. Weird.
3) Singing and Hiccups. Got laughed out of choir for this. Fuck you, choir.
2) Worrying that you're hurting someone while totally mashing their soft bits. Mostly talking about sex again. Sometimes, when you're in 'trucker needs a sammich' mode and you're really railing on someone's twat, they make a move, or a noise, or a smell, and you think, "Am I totally hurting this person right now? Do they just not want to stop me out of politeness?" This is a weird spot, because you could power through and try to finish quicker out of courtesy, but that means increased punishment. Or you could stop and ask if they're okay, which is bad if they're about to blow it. Also, you look like a sensitive vag, which is fine at times, but not in the middle of taking someone to the outskirts of bonetown to bury them in a shallow bonegrave.
1) Chatting over the internet while masturbating. Technically, I have the courtesy to take my cock out of my hand if I have to communicate with a loved one or relative while amidst the shady, shameful cloud-cover of self annihilation. But there's still a filthy naked woman in another window on my computer, and possibly some dogs and midgets and that video of elephants tromping on tutus that I like so much, so it's still pretty uncouth.
Short Answer: Big surprise that most of this is about bodily functions. Hey, I just did sarcasm while masturbating!