118 to 212 days, give or take some encounters
Travel times depend reliably only on one thing: the existence of a phlogiston river. Helm operator level matters for ship speed only at tactical speeds, not over long distances, so we can disregard navigator level (Spelljammer boxed set, Concordance of Arcane Space, p. 35). Rivers have directional flow, so only rivers that flow from your origin to your destination are useful; few rivers are bidirectional. Travel through the disordered, non-river phlogiston is dangerous and more than twice as slow on average, assuming you arrive at all.
Greyspace and Realmspace are fortunate: a river flows bidirectionally between them (sidebar spanning pages 86 & 88), making travel possible and relatively easy from Oerth to Toril. The time to travel through the phlogiston from any Sphere’s wall to any other Sphere’s wall is variable, depending on unknown factors, and ranges from 10 to 100 days (p. 54) (disregarding, as you say, whether conveniently-placed portals are currently available).
Travel within the Spheres depends on whether you encounter trouble that delays you (p. 72–3), and where you enter the destination Sphere (which is random), which determines how far you are from the destination planet. We'll ignore encounters for now in order to determine a baseline of travel times. Where you leave your origin Sphere is presumably the closest sphere wall to the origin planet's current location, unless factors interfere with the direct route, so we can use minimum distance there.
Spheres have a diametre twice the orbital diametre of the outermost planet (p. 52). Per Appendix 2: Travel Times, Oerth to The Spectre is 40 days, and Oerth is the centre of Greyspace, making it 80 days to the sphere wall. In Realmspace, Toril is the third planet out, and its minimum travel time to H’Catha is between 14 days (closest approach) and 18 days, giving a minimum days’ distance from a random location on the sphere wall of 28 days, or (given that Toril is 2 days from the Sphere's primary/centre, an orbital diametre of 4 days) 28 + 4 = 32 days at worst if you enter the Sphere on the far side of Toril’s orbit. For such a long distance we're ignoring takeoff and landing times in gravity wells, since they're on the order of tens of minutes (p. 53) and are less than a rounding error.
Given convenient portals in both Spheres’ crystal walls, and given a lack of interesting encounters (both big ifs), we can calculate a baseline travel time from Oerth to Toril at 80 days (Oerth to Greyspace wall) + 10–100 days (phlogiston river) + 28–32 days (random Realmspace entry point to Toril) = from 118 to 212 days.