This soap may be a good fit for addressing the oily scalp portion of your concern. Its formula is described as providing a deep cleanse, which can help remove excess oil and the heavy feeling that builds up at the roots. Ingredients like nettle, horsetail, and burdock root are often included in products aimed at creating a cleaner, lighter feel on the scalp.
For the dry ends, caution is needed. The thorough cleansing action could potentially make already dry hair feel rougher or more brittle. To use it effectively, try applying the lather primarily to your scalp and roots, avoiding the mid-lengths and ends as much as possible. Let the rinse water carry a minimal amount of cleanser down the hair shaft. It's highly advisable to follow with a conditioner or hair mask specifically on the mid-lengths and ends to replenish moisture and soften the hair. The panthenol in the soap can help somewhat with reducing roughness, but for significant dryness, additional conditioning is necessary. You might also consider using this soap less frequently, alternating with a moisturizing shampoo.