You could also use this,
sed 's/^\([^<]*\)<.*>\(.*\)$/\1\2/g' file
^\([^<]*\)< - Fetches any charcter not of
< zero or more times from the starting position upto
< and finally stores the fetched characters into a group.
.*> - Matches any character zero or more times until it finds
\(.*\)$ - Once the sed finds
> character, it starts to store all the characters which are next to
> upto the last into another group(stores characters inbetween
sed prints only the stored groups(
\2) through back-reference.
$ cat file.txt
FOO<td align="right" style='mso-number-format:"\[$-409\]m\/d\/yy\\ h\:mm\\ AM\/PM\;\@";' x:str>BAR
$ sed 's/^\([^<]*\)<.*>\(.*\)$/\1\2/g' file.txt