Has anyone implemented wireless networking over walkie talkies?

Ideally with several pairs, ie teaming several dial-up links over pairs of walkie talkies?

Yes, tone packages are about the only way. You'd need some device on each end. I doubt you could get much of any speed. Even with military type stuff it is hard to get much speed over tones. A very good system might support a 32 bit word but I doubt you could get more than 16 tone packs in a walkie talkie. Then you have the PTT deal to play with.

Any suitable hardware for this?

Or are you talking about the standard sound card, a speaker and a microphone?

This sounds like HAM stuff - there may be laws in your area regarding doing this sort of thing via walkie talkie. Might want to make sure.

I don't know if this can be done with walkie talkies, but you may want to have a look at packet radio.

I doubt your sound card would work stock but it may be possible to route your signal to it via some program. Well, it actually could work now that I think about it. Never heard of a program but someone here could make it maybe.

You could make a device, as above ham and other electronic buffs have made that stuff. Maybe some old Popular Electronic mag would have it.

There are old modems out there that take audio and convert to some old standard. I doubt you'd get any of the newest stuff to work.

Ham stuff may be out there along with surplus.

As stated it depends on the communications regulations for your country. Here in the US the common services like General Mobile Radio Service (GMRS), Family Radio Service (FRS) AKA common walkie talkies and Citizen Band (CB) it is illegal to transmit non voice data of this type.

This is similar to certain modes of Amateur Radio i.e. Ham stuff and to transmit over ham bands requires a license.
FYI it is a fun and can be an extremely varied hobby.

In the US, what is the legal option for data transmission over radio that has the LONGEST RANGE?

Licensed amateur(Ham) radio.

No one has been arrested by using a CB wrong in the last 50 years. But what they say is basically correct.

Shortwave (ultra low) would be longest but you'd have to be a pirate station have have access to a million watt system.

How far do you need to go?? Some companies took over a line of sight tv system and they now use it for data. They sell that pretty cheap in some areas.

I think data IS allowed since remote control cars work on CB which is non voice.
The only time anyone ever gets in trouble with CB is then they run way to many kilowatts near neighbors.

Ok, so there is only one 27MHz RC channel that is shared with the voice band. RC is limited by output power so interference is unlikely. What the OP is asking about IMHO is illegal on CB.

Another option which might be easier to implement would be wireless RS-232. These would basically have the same range as walkie talkies and be just as fast. No license required. However, even though they can be connected similar to a wireless router it isn't the same so one would require more hardware.