Can I use 1 speaker for both by radio (Becker 3201) and vario (LX160).
Both call for a 4ohm speaker.

Strictly speaking no.

Would connecting both to one speaker still work ?

No

Would it be too quiet ?

That's not the problem

Any chance for damage to the radio or vario ?

Very much so.

There are a couple of options

1 - A 2 channel mixer and reamplifier driving one speaker.

2 - Feed the vario audio ( suitably attenuated ) into the audio /
intercom input of the radio. The radio amplifier then drives the speaker
with the vario audio until the radio breaks squelch and you hear the
radio signal.

3 - Simplest solution ........... Two speakers.

Ian