Many of the homes of the time had a courtyard around which were situated various rooms. The courtyard was used for cooking and eating. In John McCray's book Archaeology and the New Testament, he has some diagrams of typical houses of the period.
The point being that to "enter" someone's house was not like it is today. The courtyard was open and people could, conceivably, wander in. In fact, later in Luke's Gospel when Jesus is brought to the high priest's house for questioning you get the sense that there are quite a few people lingering in the courtyard (see Luke 22:54 and following). For example, Peter is in the courtyard, seemingly uninvited; i.e. he doesn't converse with the high priest, but also denies knowing Jesus. No one seems to think it odd that he's there, per se.
One other note is the eating position during feasts ("reclining at table"). The participants would have leaned forward on their left arms, eating with their right hands (the left hand being reserved for sanitary uses, which is why it is considered rude in some cultures even today to use one's left hand for food). The point, though, is that Jesus' feet would have been behind him, making it easy for the woman to anoint them.
A fascinating article about eating customs of the time is at this link.