The most apparent parallels between Oden and Zoro are their strengths as swordsman. Oden is the strongest swordsman the cast of Wano witnessed, so if Zoro is to become the strongest swordsman, he would be compared to Oden to some degree.
His quest in Wano up until now seems more geared towards highlighting what the country has lost rather than a direct tie to Oden.
When we entered Wano, the country lost power and honor. Ashura Douji became disillusioned at the state of the country because he was the only Scabbard, as far as we know, who's been there to see its complete rot in real time. And to him, all the strong and honorable warriors are either imprisoned or dead.
And here comes Zoro who, despite his aloof nature, is a strong and honorable fighter. He embodies the values once found in the country. Wherever he goes, people with deep understanding of what the country was and who inhabited it took notice.
Yasu once led the proudest samurai of the country. He could tell immediately Zoro was a special case. Kawamatsu initially believed Zoro to be a fool who had no right to take Enma until he was that impressed by Zoro's strength display. He'd also be indebted to Zoro for looking after Hiyori in his stead. Hiyori has had to surround herself with the worst scum after separating with Kawamatsu, so it only makes sense she develop respect and trust for him. Momonosuke desires to live up to his father as both a warrior and leader. It's natural he take a shine to Zoro as a role model.
This treatment hasn't been limited to Zoro either, Luffy has had a positive effect on the people of Wano in a similar fashion. He helped restore Hyogoro's spirit, was the one to push Momo to get his act together, and rallied the prisoners of Udon. He's even gained Ashura Douji's attention when he stood up to Kaido.