The density of steels ranges from about 7.7 to a bit over 8.0 g/cm^3, depending on the specific type. Some of the tool steels (a group that contains alloying elements such as cobalt, molybdenum, and tungsten) and some of the stainless steels tend to be the most dense.
Steels are a very large family of alloys, having in common that iron is the principal ingredient (They are iron-based, and ALL steels are mostly iron, by definition. Nickel-based superalloys such as inconel and hastelloy are therefore not steels).
There are other elements present in steel - usually carbon, at a minimum. The range of carbon content for ordinary steels runs from a trace (~.1% or so) up to a maximum of 2%, theoretically, though actual carbon contents above 1% are fairly rare.
Many other elements may be added to produce various types of steels having specific properties. In corrosion-resistant steels, carbon is usually present in only minute quantities, with chromium (400 series) or chromium plus nickel (300 series) being the major alloying additions. In the 400 series grades that can be hardened by heat treatment, hardening is accomplished though the combined effects of the carbon and chromium. The 300 series alloys can be hardened (and strengthened) only through cold working (strain hardening).
Density has no direct relationship to tensile strength, BTW.