Carina,
What version of ArcGIS are you using?
Based on your comment about the Define Projection tool, I am wondering whether some data layers now have incorrect coordinate systems (projections). For instance, for the rasters that have cell sizes in degrees, what coordinate system do they have? They should have a geographic one like WGS84.
Even if the layers are all using a geographic coordinate system, and the data frame is too, the measure tool should default to measuring geodesic distances and some linear unit.
Because of that, I am wondering whether data frame/layers have projected coordinate systems, but the data (coordinates) themselves are still in degrees.
Melita