I'm searching for proper expressions that mean connection of RNA strands. Up to this time I came with strands connection, strands conjunction, and strands ligation.
Are my expressions proper, or do you know other expressions?
Almost certainly ligation is the preferred term here; note that the enzymes that actually connect the strands are termed ligases, which immediately suggests the preferred word for the action they perform. I would strongly lean away from conjunction, which suggests to me a word more suited to the particular orientation two strands of RNA might have towards each other, and certainly doesn't immediately suggest the physical connection I think you're implying in your question. Connection also seems a weak word to use, because it does not convey the aforementioned physical joining together of the strands of RNA; if one used it, it might be ambiguous whether the strands are actually ligated to each other or simply associated together in solution, through weak ionic bonding or some such.
Finally, as a word of advice, you shouldn't really seek a reply to this sort of question at an English language site; technical terms often morph from their intended meaning when they are first coined, to a more precise and different meaning later on as the science advances, so that one might be mislead if one tries to divine the technical usage from the meaning in ordinary language -- the stuff this StackExchange specializes in. (In just one example, the TCS site recently hosted a question about what they would might rename the method dynamic programming if they had a choice in the matter; debates like this often occur quite often in the mathematical sciences, subjects in which this forum has no expertise.)