You can install vinyl (linoleum is an antiquated product) flooring with a water based adhesive that hardly has any odor & is safe around birds (just be sure to roll out all bubbles with floor roller or hand roller).....also, today you can install a loose-lay vinyl (no glue)...you just remove & reinstall the shoe moulding or base moulding after you lay & trim the vinyl, to keep the edges from curling.....don't forget to lift and/or replace thresholds & doorsills to finish those edges.....
Linoleum used to be installed with petroleum based adhesives.....
One other thing, if you can see the impression of any old nailheads in your current flooring, remove them & replace with flooring screws, being careful to make sure the screws are perpendicular to the floor & heads are flush with the sub-floor.....simply hammering old nails back down will allow them to work back up & most likely damage your new flooring.....
Be sure you use the proper trowel, with the notching specified on the label, if you install yourself & if you have it installed, make the installer show you the glue & insure it is water based before they install.....