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:
私は難しい仕事でもする
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.)
私は難しい仕事もする。
I'll do difficult work as well.
(This sentence implies that there is both difficult work and easy work.)
私はこんな難しい漢字も読める。
I can also read difficult kanji.
(This sentence implies that there are both difficult kanji and easy kanji. For example: a newspaper article.)
私はこんな難しい漢字でも読める。
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:
私はこんな難しい漢字も読める
, with the translationI can read even difficult kanji like this
(pg 250). So assuming these are accurate, my question is whether でも can be substituted in without a change in meaning.