I think the reason behind you are facing wget error is your OpenSSL might be receiving something else other than the
ServerHello in your protocol version it understands from your server. It is very possible that it is happening because the server is trying to answer with the plain HTTP which is unencrypted. It can also start appearing if your server is only supporting the TLS 1.2 and your client is somehow unable to understand that protocol version. Normally now a days all the servers are backward compatible to at least the SSL 3.0 / TLS 1.0 but I guess your this specific server is not.
I had also faced this issue as I had not enabled my sites 'default-ssl'. Only the '000-default' was listed in my
So to enable the SSL site on Ubuntu 14 LTS, Apache 2.4.7 I used below commands:
service apache2 reload
Hope it helped you to fix wget error.