Sudoku: Odd Bonds

^{An entry in Fortnightly Topic Challenge #47: Wacky Sudokus.}

^{Edit: Clarified three of the rules.}

Rules:

• Normal sudoku rules apply.
• Inside the sudoku, there exists one "loop".
• The loop consists of only odd numbers. However, not all odd numbers (i.e. cells with odd numbers in them) are part of the loop.
• Box 5 (the central 3×3 box) is the only box that does not contain a part of the loop.
• An odd number that is part of the loop must be orthogonally adjacent to exactly two odd numbers. (i.e. if cell A shares an edge with cell B, but cell A also shares another one of its edges with cell C, then cell A is said to be orthogonally adjacent to cells B and C.)
• An odd number that is not part of the loop can be orthogonally adjacent to any number except odd numbers that are part of the loop.
• In the dashed cage, the number (read from left to right) is divisible by 7.

For convenience, here is a link to the sudoku.