How do I make a paper white again?
One approach would be to use various solvents. You would require solvents in which your various stains were soluble in. Alcohols / water would be suitable to dissolve the soda. Whereas an organic solvent would be suitable for washing away the gasoline. Though gasoline is typically colourless.

Another approach would be to expose the paper to copious UV irradiation, materials are coloured due to absorptions in the visible spectrum which trigger electronic excitation. These absorptions bias the transmission and reflection of otherwise white light and give the materials their colour. UV radiation is of higher energy than visible light radiation, and therefore the chemical excitations involved can prompt reactions which result in the destruction of the materials themselves.

A similar approach to invoke this chemical degradation of the coloured materials could be achieved through using a strong acid or base. This would be akin to the effect of bleach on household surfaces. Again, exposure to acids and bases can prompt reactions which result in the degradation of coloured materials.

It is worth noting that all of these methods will have some affect on the paper. Continued washing / drying of the paper with solvents will likely cause the paper to become brittle and affect the absorption of the paper, which may affect your ability to write / print on it. A similar effect may be noticed under UV irradiation, though I expect it wont be to the same extent.

A sufficiently strong acid or base may be able to completely degrade your paper as well as your coloured contaminants.