Wendy, most types of adhesive can be handled with removers available at Home Centers. But none get glue all the way out of the grain. Be prepaired to sand you hind end off, otherwise, when restaining, the glue will be evident.
First try a Home Center recommended adhesive solvent and a gentle hand at a putty knife as not to scar the wood. The adhesive removers will ruin the existing stain. Rent a hardwood floor sander (two types - one for the bulk of the floor, one for the edges/corners) remove the moulding (to get as close to the wall as possible - new moulding will cover the difference)and sand like a bugger.