The Collaborative International Dictionary of English v.0.48:

Stroll \Stroll\, v. i. [imp. & p. p. Strolled; p. pr. & vb. n.
   Strolling.] [Cf. Dan. stryge to stroll, Sw. stryka to
   stroke, to ramble, dial. Sw. strykel one who strolls about,
   Icel. strj?ka to stroke, D. struikelen to stumble, G.
   straucheln. Cf. Struggle.]
   To wander on foot; to ramble idly or leisurely; to rove.
   [1913 Webster]

         These mothers stroll to beg sustenance for their
         helpless infants.                        --Swift.
   [1913 Webster]

   Syn: To rove; roam; range; stray.
        [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

142 Moby Thesaurus words for "strolling":
   ambling, ambulant, ambulation, ambulative, ambulatory, backpacking,
   cautious, circuit-riding, circumforaneous, circumspect, claudicant,
   crawling, creeping, creeping like snail, deliberate, discursive,
   divagatory, drifting, easy, errant, expeditionary, faltering,
   flagging, flitting, floating, foot-dragging, footing, footing it,
   footloose, footloose and fancy-free, footwork, fugitive, gadding,
   gentle, globe-girdling, globe-trotting, going, going on foot,
   gradual, gypsy-like, gypsyish, halting, hiking, hitchhiking,
   hitching, hobbled, hobbling, hoofing, idle, indolent, itinerant,
   itinerary, journeying, landloping, languid, languorous, lazy,
   legwork, leisurely, limping, locomotive, lumbering, marching,
   meandering, migrational, migratory, moderate, moving, mundivagant,
   nomad, nomadic, on tour, passing, pedestrian, pedestrianism,
   perambulating, perambulation, perambulatory, peregrinative,
   peregrine, peripatetic, pilgrimlike, poking, poky, progressing,
   rambling, ranging, relaxed, reluctant, roaming, roving, sauntering,
   shifting, shuffling, slack, slothful, slow, slow as death,
   slow as molasses, slow as slow, slow-crawling, slow-foot,
   slow-going, slow-legged, slow-moving, slow-paced, slow-poky,
   slow-running, slow-sailing, slow-stepped, sluggish, snail-paced,
   snaillike, staggering, straggling, straying, tentative, thumbing,
   thumbing a ride, toddling, tortoiselike, tottering, touring,
   touristic, touristy, traipsing, tramping, transient, transitory,
   transmigratory, traveling, treading, trekking, trudging,
   turtlelike, unhurried, vagabond, vagrant, waddling, walking,
   wandering, wayfaring