Yes, they are grammatically correct, and yes the nuance is different.
「も」implies that there is a list, and that the stated item is just one item in that list.「でも」could refer to the item in isolation. So in the example sentences:
Even if the work is difficult I'll do it.
(This sentence implies that there is difficult work, but that there may not be any easy work.)
I'll do difficult work as well.
(This sentence implies that there is both difficult work and easy work.)
I can also read difficult kanji.
(This sentence implies that there are both difficult kanji and easy kanji. For example: a newspaper article.)
Even if the kanji is difficult I can even read it.
(This sentence implies that there are difficult kanji, but that there may not be any easy kanji. For example: classical Japanese texts.)
These interpretations are supported by the following unofficial sources: