Leviticus 2 The grain offering was about gratefulness and worship. Israel was told to bring these sacrifices once a year -as a sign of thankfulness during The Feast of the Harvest- or else any other time that they felt particularly thankful. This would have been the main sacrifice that would have provided bread to the priests, making it sort of like a tithe. This offering reminds us that God controls the drought and the harvest, the time of plenty and the time of need, and is to be thanked when our times of plenty come along.
Leviticus 3 The peace or fellowship offering came with a pretty cool side benefit for the Levites: Israel was allowed to offer the priests some loaves of leavened(!) bread during the communal meal that followed (Leviticus 7.12-15). If the priests had kept a bread cutter anywhere around, this could have been where the traditional male's beloved steak sandwich was first invented. Like the fellowship offering, the Jesus' sacrifice brings us into community with one another, enabling once-strangers and even former enemies to sit down and share a common meal in His presence.
Leviticus 4 The sin offering was for unintentional sin, involving everyone from the High Priest -because ministers make mistakes, too- to the poorest common Israeli citizen. This sacrifice brought forgiveness to the one who offered it. Now, I have got two quick observations. (1) The High Priest's sin brings guilt on the people - as the leader, his sins have an impact on everyone else, so his offering is the same as what the whole congregation of Israel would have offered together - Leviticus 4.3,13-14 (2) God holds leaders to account (see point #1) but He also does not burden poorer worshipers too severely; Leviticus goes down the list of wealth offering smaller sacrifices ranging from bulls, to male goats, to female goats, to doves, to flour which would soak up some blood from the altar and act as a very cheap sacrifice. Like the sin offering, Jesus covers even our unintentional sin, and unknown sins, sins of which we are not even aware.