wget gives error "dyld: Library not loaded: /opt/local/lib/libnettle.4.dylib"
I think you have both MacPorts and Homebrew installed. MacPorts installs by default in /opt/local, whereas Homebrew installs in /usr/local. Since the command you are actually running is /opt/local/bin/wget, you probably have /opt/local/bin before /usr/local/bin in your PATH environment. Check it with:

$ echo $PATH

In such a case, any software installed with Homebrew is not used at all, if not called with its absolute path. So, try launching Homebrew's wget with its absolute path:

$ /usr/local/bin/wget 

If it is working in this way, put /usr/local/bin as first folder in your PATH environment, by modifying ~/.profile or ~/.bash_profile file.