While not exclusively Russian, the IPhO problems are heavily influenced by the Russian school. The official site hosts PDFs of all past IPhO problems and solutions from 1967 onward. Since Russia is a dominant participant, many "Russian-style" problems appear here.
A legendary set of PDFs compiled by the coach Anatoly Zilberman. This collection contains over 1,000 original Russian olympiad problems from 1970-2005, categorized by topic (mechanics, electrodynamics, oscillations, etc.) with complete solutions. This is the single most sought-after Russian physics olympiad problems PDF collection. russian physics olympiad problems pdf
Many free PDFs circulating are low-quality scans. While not exclusively Russian, the IPhO problems are
If you want clean, diagram-included, fully solved collections, consider: If you want clean
The official website of the Russian Olympiad movement. Navigation requires some Russian, but you can use browser translation. Look for the section "Задания и решения" (Assignments and solutions). They offer official PDFs for all four levels, including answer keys.
Not exactly an Olympiad book, but Irodov’s 1,000+ problems are the unofficial Russian Olympiad boot camp.