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The type of respirator that is known to be strongly resistant to oil is P respirators. P respirators, which include NIOSH-approved models like P95 and P100, are specifically designed to offer protection against both solid and liquid aerosols, including those that are oil-based. The "P" designation stands for "Power," indicating the respirator's capability to filter out particulates that could be found in various environments, including those where oil is present.

In contrast, other categories like N respirators are not resistant to oil and are intended for use in environments free from oil aerosols. R respirators, while providing some level of resistance to oil, have limitations and can only be used for a limited time when oil vapors are present. P99 respirators offer a similar level of protection to P95; however, they are not as widely recognized as the P series as a whole. Therefore, P respirators are the correct answer due to their robust design specifically suited for oily substances, ensuring adequate protection for the user in relevant conditions.