The work covers the characteristics of the functional properties of composites bordering thermoplastics and elastomers. The research is a continuation of considerations on blends in the form of a mixture of natural rubber (NR) with an ethylene–vinyl acetate copolymer (EVA) and the addition of a lignocellulose biofiller (wheat straw). After describing the processing and rheology as well as examining the thermal properties and morphology of composites (Part 1), the second part focuses on the characteristics of their performance. The effect of both different ratios of mixed polymers and the amount of filler on tensile strength and elongation at break, resistance to thermo-oxidative aging, hardness, tear resistance, barrier and damping properties, as well as flammability were investigated. The increased EVA content has shown a positive effect on tensile strength, elongation at break, resistance to thermo-oxidative aging, hardness, relative damping, tear strength, barrier and burning delay. On the other hand, a larger amount of natural rubber provides high flexibility and promotes the creation of a reinforcing structure by the filler used. Moreover, a significant impact of the addition of cereal straw on the barrier, damping, strength and flammability properties of composites was also noted. The great advantage of the prepared compositions in relation to commercial plastics is their environmental friendliness, primarily by replacing some petroleum derivatives of plastics with natural rubber and straw fibers.