This computer is not connected to internet but still I have managed to be infected with some viruses. I am really puzzled how that happened because this computer is only used to write some texts in word and only thing that is gets to computer from outer world are some Word documents. Could it be that computer is infected through Word document?
It is very possible. Word documents, as all other office documents, are one of the favorite transport methods for viruses and other malicious software. If you have any interaction with the rest of the world on that computer (let it be only bringing documents from other computer like you) then you absolutely need some antivirus software and antispyware. Updates can be little tricky on computer that is not connected on internet, but you always can download updates on another one and bring them to this computer on USB flash drive or CD.