Well, the answer I would give strongly depends on the degree of automatization (patter recognition?) you need or want for this process. Thus, it is a question of the budget you have available for new software.

For example, for manual lithological correlations I use the multi-well modul of WellCAD (Alt: Link 3). Colleagues of me are using an addon of petrel (Schlumberger: Link 1) or an addon of the JewelSuite (Baker Hughes: Link 2) to solve similar work. However, investment costs for these examples differ significantly.

UPDATE: Regarding the second part of your question. Lithological correlations by comparison of log pattern between well locations are often performed using the volume fraction of shale (calculated from the gamma ray log or SP) as lithological indicator/descriptor. Additional logs can be very helpful to strengthen your results. Publications to be recommended are standard textbooks like:

Book: Fundamentals of Well-Log Interpretation - The Acquisition of Logging Data

Oberto Serra

edited by Oberto Serra, 01/1984; Elsevier., ISBN: 978-0-444-42132-6

or

Book: Basic Well Log Analysis for Geologists

G. B. Asquith, Charles R. Gibson

01/1983; American Association of Petroleum Geologists., ISBN: 0891816526

http://www.software.slb.com/products/platform/Pages/petrel.aspx

http://www.bakerhughes.com/products-and-services/reservoir-development-services/reservoir-software/jewelsuite-reservoir-modeling-software/jewelsuite-geologic-modeling-software/well-correlation

http://www.alt.lu/software.htm

Dear Sven Fuchs,

Thank you for your valuable answer.

Maybe you can do what you want using clas plugin for opendtect

www.opendtect.org

they provide free licenses to universities

You can also use ROCKWORKS borehole utility. It is fantastic.