Bob: "No one lies."
It can be true if and only if (iff) all other statements are true.
Jennifer: "No one tells the truth."
It can be true iff all other statements are lies.
Thus, Bob is definitely lying.
Also, she must not be speaking truth; because by universal quantification,
'Nobody speaks truth' means she is also not speaking the truth.
Conrad: "Jennifer is not a liar."
As shown above, Jennifer is indeed a liar. Thus this is not true and Conrad is also a liar.
Tom: "Conrad and Sherry always lie at the same time."
If this is true, Sherry is also a liar from the previous one.
If this is false, Sherry is not a liar.
We'll deduce it from further statements.
Here comes the little loop...
Sherry: "Danny never lies." (let's call it statement S)
Danny: "Sherry is a liar." (let's call it statement D)
S can be true iff Danny always speaks truth (assuming that Danny says something and not keeps silent).
If D is a true statement, then it would be ok (Sherry is lying about Danny never lying). But if it is a lie then it becomes unclear, whether Sherry is a liar and/or Danny is a liar.
Then comes the last but not the least :
Adam: "Danny sometimes lies."
Again, we cannot quantify
sometimes. If this is true, then Danny is also a liar(the one who doesn't always lie)! But, he is not lying in this case.
And as it goes, in statement D, Danny speaks truth. Which must make Sherry a liar.
Also, this means Tom is not lying.
This makes Adam a knight!!
$4$ people are lying in the given statements.
Bob, Jennifer, Conrad, Sherry
Danny(in the given statement), Adam, Tom