There are a couple paths you can take to solve this problem:
- A hardware only solution. It's simple to implement, strong and features and equally strong (high) on price.
- Software based KVM with some bodging to address the audio needs. If you can live with some manual switching of USB and audio, you've got a strong solution here.
A Proper KVM
Something that's definitely not in the consumer market is a KVM that handles multiple computers, dual headed high-res display and audio. There's lots of gimmicky firms out there, but to do it right, you need something like the Avocent SV300. It checks off all of your requirements: supports UHD 4K Resolutions in a dual headed configuration, audio and your USB devices. It's not cheap at about $800USD. However, this is that piece of kit that you gawk over when you go into a broadcast studio or a big dev shop and watch them seamlessly move between their multiple computers.
Disclaimer: I used to work for a company† that was acquired by Avocent and have many years experience with their KVM and secure console servers (RS232/RS422 over IP). I've even used their digital signage products when I was with other companies so I'm quite familiar with them and their capabilities.
An Open Source Solution
There's an FOSS KVM solution that is probably well worth looking into. It's called Barrier and I've mentioned it in a couple answers here on Ask Different:
The one area you'd likely have issue is the audio. For that, you would need a simple, inexpensive audio source switcher. Basically, it's a four input, one output switch that you'll connect to your headphones.
The upsides here are this is very inexpensive. This will require some time and very little in the way of hardware (the audio switcher). The downsides are that the audio is manually switched (minor) and there's no USB switching (could be major depending on your requirements). There are USB switches available, but this is where it starts becoming a bodge. Instead of an all-in-one solution like the Avocent, you've got a minimum of three different disparate solutions and one being open source.
Since this is software and it requires you to go over your network (I'm assuming all the computers are on the same network), your video performance will be limited. The performance will be like using a remote desktop app like VNC or RDP. A wireless network is good, a wired network will definitely be better. If you're hoping to do video editing and/or gaming, this probably won't work.
Barrier Configuration Screen
A note on the cheaper KVMs
There are some cheaper KVMs that you can find online from IOGear, TrendNET, and StarTech. I wouldn't say that they are bad, because they're not. If you're working a dev environment in mostly text or lower resolution graphics, you can certainly use these; so don't rule these out. However, all these new video standards are bandwidth hungry and being able to accommodate all of that bandwidth and provide you with smooth experience requires quality components and some strong engineering. In the end, you get what you pay for.
† I worked for Equinox Systems (no, not the fitness club or water filtration MLM company), a direct competitor to Digi International that made RS232/RS422 and UART over IP products that spanned applications from Unix, Solaris and even Citrix. It's here I gained my in depth experience with these types of products.