IPUMS National Historical Geographic Information System (NHGIS) - https://www.nhgis.org - has census summary tables from 1790 through the present, including age/sex/race tables for your years of interest. (ACS 2019 5-year tables are coming soon, too.) NHGIS also has "time series tables" that link comparable data from multiple censuses, including some age/sex/race tables spanning 1980-2010, using the finest-grained age & race categories available for that period.
For these years, there aren't many tables that break down by age/sex/race and nativity, but you can use the NHGIS Data Finder to explore what's available.