Change the locks. Like you say a lot of people have had keys. It is quite normal - but the family will expect to each get a set.
Contents. Suggest a fair mechanism and, if they wish, let everyone suggest an alternative. Vote. It will soon sort out the issues.
Another suggestion - make a list and ask everyone to nominate the things they would hold most dear ( a much nicer way of saying who is the most grabby!)
If several people want the same things then it is a lottery- names in a hat for each item. If there is no contest and everyone is happy, sorted.
If it is anything like most families, there will only be 10 at most things that will be an issue - Waterford glass, the pretty tea set that has not seen the light of day in more than 20 years, that particular photo ( hint: get copies so everyone gets a copy) etc.,etc.
mf