Are you sure about the Eiffel Tower being closed? I looked on their FB page and they show open and the only thing on their official website is this:
"Saturday, may 18th : due to the arrival of the Ecotrail run, the stairs are closed to the public at 3h30 PM. We apologize for the inconvenience."
Wondering where you saw they are closed?
There are certain arrondissements where the garbage workers are picking up as usual. Balso, I think, gave a website which I will search out in a minute for you.
I'm going to be there mid-April for 10 days. I'm staying in the 7th where I usually stay and have no plans to change at this time. I've allowed myself some flexibility in days on train journeys to Paris and from Paris to London in case of strikes but I did that before I knew there were going to be strikes. The protests are in isolated areas - usually a large square where a lot of people can gather. You can easily avoid the protesters if there happen to still be protests when you are there.
editing to add: Here is the link Balso posted elsewhere. The green zones use the City of Paris sanitation workers and are where there are strikes. The other colors use private collectors and are not on strike.
2nd edit: I was just able to go thru the official ticketing site to the point where I put in my CC for a 2nd level visit on April 19 at 5PM so tickets for April are being sold. Many other days in April have the hatch marks on the calendar meaning they are sold out.