This snippet on the Advanced Bash Scripting Guide says:
# The == comparison operator behaves differently within a double-brackets
# test than within single brackets.
[[ $a == z* ]] # True if $a starts with a "z" (wildcard matching).
[[ $a == "z*" ]] # True if $a is equal to z* (literal matching).
So you had it nearly correct; you needed double brackets, not single brackets.
With regards to your second question, you can write it this way:
HOST=user1
if [[ $HOST == user1 ]] || [[ $HOST == node* ]] ;
then
echo yes1
fi
HOST=node001
if [[ $HOST == user1 ]] || [[ $HOST == node* ]] ;
then
echo yes2
fi
Which will echo
yes1
yes2
Bash’s if
syntax is hard to get used to (IMO).