Examples of using both:
Inverter: Let's say you have a pair of mono phase shifters, and you'd like to use these to create a signal that pans its phasing. To do this, you would mult your audio to both phase shifter inputs so that each one has the same signal to process. But when feeding the phase shifters with a single LFO for modulation, you'd first split these as well, but then one LFO split goes through an inverter before the phase shifter, while the other goes in to modulate the other phase shifter as normal. The result will be that when the first phase shifter is at the top of its sweep, the other is 180 degrees opposed and is at the bottom of its sweep. Also, in audio inverters can have a very neat use with effects; you can use a mono reverb to put a typical reverb effect on an audio signal, but before the reverb you'd mult the audio. One mult goes on to the reverb, and the other to an inverter, and both signals come back together in a mono mixer. In this usage, the inverted audio will cancel the "dry" part of the reverbed signal...but will also partially cancel similar waveforms in the reverb's output. As opposed to cranking the reverb to 100% wet, this method creates more of a "ghosted" signal, with the cancellation of the similar waveforms in the resulting mixer output becoming less and less as the reverb processes the zero degree signal with a certain degree of imprecision.
Adder: These are the reliable method for adding offset voltages to CVs. Let's say you have several VCOs fed from the same CV. This goes through an adder before splitting. Then, you have a sequencer, and you want to transpose all of these VCOs identically with it. The messy way would be to feed the VCOs directly. But the right method would be to use a precision adder to combine the incoming CV with the sequencer CV, then split the adder's output, as this gives you a lot more control, a simpler signal path, and as long as your sequencer CV out has quantizing, you can transpose the VCOs in exact steps to anything you prefer while at the same time maintaining proper CV control from your own local controller, MIDI, etc. Simple, straightforward. That example is one of what's probably countless uses for these.
Lastly, line level audio in Eurorack. Yes, you need a preamp. Audio signals within the modular environment are several times higher than typical line level signals, plus the impedence difference between your external source and the modular can also be a detriment that a good input module can correct. Another reason for having an input module is that many of these also have envelope followers, which allow you to take the dynamic information in an incoming signal and extract that to a CV, and these prove invaluable when using the modular as an external signal processor...such as in using the incoming dynamics to sweep a VCF in tandem with the external signal's peaks. Plus, a good preamp with isolation helps keep ground loops out of the synth; conversely, this is also why you should have output isolation, in addition to stepping the synth levels back down to line level.