Polar-functionalized polyolefins are high-value materials with improved properties. However, their feedstocks generally come from non-renewable fossil products; thus, it requires the development of renewable bio-based monomers to produce functionalized polyolefins. In this contribution, via the Pd-catalyzed telomerization of 1,3-butadiene and three types of bio-based alcohols (furfuryl alcohol, tetrahydrofurfuryl alcohol, and solketal), 2,7-octadienyl ether monomers including OC8-FUR, OC8-THF, and OC8-SOL were synthesized and characterized, respectively. The copolymerization of these monomers with ethylene catalyzed by phosphine–sulfonate palladium catalysts was further investigated. Microstructures of the resultant copolymers were analyzed by NMR and ATR-IR spectroscopy, revealing linear structures with incorporations of difunctionalized side chains bearing both allyl ether units and polar cyclic groups. Mechanical property studies exhibited better strain-at-break of these copolymers compared to the non-polar polyethylene, among which the copolymer E-FUR with the incorporation of 0.3 mol% displayed the highest strain-at-break and stress-at-break values of 940% and 35.9 MPa, respectively.