Will a instrument cluster from a 1998 Sunfire work on a 2003 Sunfire?

no

95-98 will work in a 95
96-98 will work in a 96-98
98.5 and 99 will work in a 98.5 and a 99 (these have digital odometers)
00-05 will work in 00-05

95-99 Sunfire and Cavalier clusters are electroncally interchangable (within the same year notes above), but they have different plugs and fit the dash differently.
00-05 Sunfire and Cavalier clusters are completely interchangeable.