The origin of many phrases are often murky because they have been in use for a long time. The phrase "Don't teach your grandmother to how to suck eggs" is at least 200 years old and is a variation along the lines of "Don't offer needless advice to an expert" - the elderly in past centuries were venerated for their wisdom and experience. One of the earliest recorded expression of this type was in 1542 -"Don't try to teach a dame to spin":

http://www.phrases.org.uk/bulletin_board/18/messages/50.html

"What do you want, eggs in your beer?" was the phrase used when someone appeared to want more good fortune than they already had. The phrase appeared in the 20th century but was popularised by GIs in WWII. One explanation was that the concoction was considered an aphrodisiac but more likely that both eggs and beer was hard to come by in wartime. (search "eggs" or scroll down about 60%):

http://www.word-detective.com/042702.html

http://www.wordwizard.com/ch_forum/topic.asp?TOPIC_ID=17907

Interestingly our holiday celebration drink of eggnog derives from centuries old recipes combining eggs and alcohol. “Nog” was an old English dialect name for strong beer :

http://www.kitchenproject.com/history/eggnoghistory.htm

The Germans also have a recipe for egg in grain alcohol called eilelikor:

http://www.sheries-kitchen.com/recipes/german/eierliquor.htm