Some in our religion feel they should learn an ancient language associated with their ancestors in order to feel greater kinship to the past. They often feel that their everyday language has become mundane or, in the case of modern English, too corrupted. It never hurts to learn another language, but which one and why?
Since this site is written in English, let's discuss that first. Long ago, the Saxons, Angles, Jutes, Franks, and others spoke a western Germanic language with dialectical differences. They could generally communicate with each other. Persons speaking northern Germanic tongues could also be understood, but with more effort. Groups of the Saxons and Angles headed across the Channel and occupied bits of Britain.
At that point, they started picking up little bits of local vocabulary. As they gradually converted to Christianity, they started adding Latin words as well. After a few centuries, the Normans took over and brought their strongly Latinized language and English was further corrupted. While these people tried to force their language on the locals, that language was just beaten until it fit the existing English structure. As a result, we do not speak French, we speak English.
Over time, English dropped the inflections that modern German still holds. It has really changed in many ways. Still, it is built on a Saxon foundation. This is why some feel that they need to pick another, less changed language.
For some, a modern Germanic language offers hope. The benefit of these languages is that there are classes and other resources readily available. In the United States, your local college may offer courses in German. A large enough college will also have courses in Norwegian, Swedish, Dutch, or even Icelandic. It is worth noting that speakers of modern Icelandic can usually read the Old Norse texts from the Sagas.
It is more difficult to find courses for the old forms of these languages. Old Norse, Old High German, Old Low German, Old Frisian, and Old Saxon are not very common. Some colleges may offer an introductory Old English class for students in their English programs. If you can't find these classes but still want to do research using old documents, Latin classes may come in handy. The enemies of the Heathens wrote quite a bit but used their Roman language to do so.
If you can't find a class, you will want to look for other opportunities. For example, the University of Iceland offers an Icelandic course online to foreign students. You can also find books to help. The Teach Yourself publishers have a book and CD set called "Complete Old English (Anglo-Saxon)" (ISBN 9780071747738) where the CDs have pronunciations.
When you decide to learn a language on your own, try to get a friend or two to learn at the same time. Even if the friend isn't a Heathen, you can usually find a geek or writer who would love to learn Old English. Having a friend help will keep your studies on track and give you feedback in pronunciations and usage. You will find yourselves communicating with each other in your new language.
All this being said, the Gods aren't particularly concerned about your specific language. Humans use language to help us form our thoughts into something useful. The Gods will tune in to your thoughts more than your grammar. On the other hand, there is a sense of otherness when you stand before the Gods of your ancestors and use words those ancestors would have spoken a thousand or more years ago.