Are Honoris Causa degree worth as much as PhD?

I think your question indicates a fundamental misunderstanding of what a honorary degree is, and who gets one. Fundamentally, an honorary degree cannot be compared to a regular PhD. All the rules for getting a PhD fly out the window, as do all the perceived benefits for doing a PhD. If you get an honorary PhD, nobody will suddenly assume that you possess the subject knowledge of the holder of a regular PhD.

Similarly, you seem to assume that an honorary degree is somehow an easy way towards a PhD. This is not the case. By and large, by the time you get an honorary degree, you either already have enough degrees or you will never need one again in your life.

Can that person be called a doctor at all?

Yes, as long as you don't pretend to have a "regular" PhD.

can an Honoris causa graduate give lectures at a university?

Sure. Everybody can give a lecture given that he gets invited or appointed to do so. In the usual case, somebody important enough to receive an honorary doctorate is also somebody that an university would love to get for a lecture.

Is it possible for one to get an honorary degree in science, or engineering

Sure.

How much demonstrated work would it take to get one?

Usually none.

An Honorary degree, which is often, but is not necessarily a doctorate, isn't really an academic degree in any sense, and shouldn't be viewed as such. They're usually given for making a mark on the world in some way - be it scholarship, public service, etc.

can an Honoris causa graduate give lectures at a university?

Do you mean teach classes? No more likely than any other member of the public that has achieved a bit of notoriety. Universities occasionally have noted writers, figures from the business community or industry scientists teach, and they don't necessarily have PhDs. If you genuinely mean give lectures - of course, as anyone can give a lecture at a university, if they're invited to do so.

Can that person be called a doctor at all?

Yes, though trying to obfuscate that into "looking" like a PhD or MD would make me think much less of that person.

Is it possible for one to get an honorary degree in science, or engineering?

Yes. These are often given to people who have made significant advances in science or engineering - for example, you might give one to a Silicon Valley-style tech entrepreneur even if they haven't done graduate work. Alternately, I've seen them given to people with science or engineering PhDs recognizing work to advance science generally.

How much demonstrated work would it take to get one?

There's no meaningful "Do X, get an Honorary Degree" threshold. It's not something you work toward, it's a recognition from a university that they think what you've done is worthwhile.

As Compass states, an honorary doctorate is not a formal credential of any kind. It can be awarded by a university on the basis of one's works and achievements, and does not require a thesis or other publications or research contributions.

Consequently, honorary degrees do not carry the same privileges as a traditional degree. You can list it as an honorary degree, but you shouldn't use it to claim you're a "Doctor." And it certainly would not satisfy the requirements of having a PhD or equivalent in a faculty search.