In websites of books and journals,logo of their publishers may be unlawful in nature, and it is displayed in websites & in their published works. What is rulings about them? Can I use these websites & read published works if I download only those what are permissible even they contain these logos?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

You are not sinful for browsing and downloading useful sites or books, even if they contain slogans that violate the Sharee'ah.

If it is possible to change such slogans after downloading the material, then you have to change them because ‘Imran ibn Hittaan narrated from 'Aa'ishah that the Messenger of Allah never left in his house anything containing the figure of a cross without destroying it. [Abu Daawood]

Allah knows best.