Does it sound strange to say "An emergency meeting is expected to be held soon." or "The new highway is proposed to be built across the swamp." Should we avoid this type of construction ?
No, there is no reason to avoid those sentences.
It is often simpler and clearer to use the active voice than the passive voice. And the active voice is especially helpful when the agent of the action is important to the message. Otherwise, the passive voice is alive and well, and there is no reason to fear it blindly.
It's all about deciding what your message is and then finding a clear way to get it across. And in that quest it is important to consider your audience or readers. In some contexts they might well expect and appreciate the passive voice.
If passive voice does not bother you, you don't need to worry about using this construction.
If passive voice does bother you, don't use it twice in one sentence unless the alternative is more awkward.
The question of doubly passive sentences is essentially the same as the question of any passive sentences. Sometimes passive voice conveys the meaning better, and sometimes it is just needlessly evasive or bland.
The sentences you've posted seem normal enough that they wouldn't stand out in conversation.