Can my transactions be traced back to me even if I do this? I installed the wallet from Bitcoin's official website on 4 computers each running Microsoft Windows 7.

Moreover on each of the 4 PCs, I installed OpenVPN client, meaning each of the computers access the internet via VPN.

Suppose I do not use an online Bitcoin mixer to further anonymize my transactions.

Instead I transfer my Bitcoins from one computer to another, all the while making sure that the VPN gateway/exit node is located in a different country.

Question: can my transactions be traced back to me?
Well, that depends. First, never reuse addresses if you are doing this.

Second, if you are not mixing, the transactions will, with no exception, be traceable. Would there be someone focused on you, he would see the bitcoins move around, and so most probably think they are spent. But if he is really interested in you, he will probably keep track of the coins and whenever you really spend one of them, he will probably notice and try to track the owner of that address to see what you did with them.

He will probably only stop keeping track of those coins if he sees them being spent by someone that cannot be you, or if he cannot track them anymore as they are split up and combined with many other coins.

You must be quite paranoid considering your few questions here. I can maybe advise you to buy bitcoins for cash like via localbitcoins.com. Apart from the guy you trade with, no one will know you bought coins.