The short answer is: no.
Ultimately the situation resolved itself when the Democrats basically gave up, saying they didn't have the votes to pass the measure anyway now. The Republicans then returned before the proposed bill would have otherwise expired. This is not even the first time Republicans (or Democrats) have done such a quorum denying walkout in Oregon in recent memory, with both parties having done it in 2001.
If the missing Senators were within the state, then yes, there are legal recourses to force their return. Rule 3.01(2) of the Rules of the Senate says
(2) If a quorum is present, the Senate shall proceed with the transaction of business. When there is no quorum present, a lesser number of members may adjourn from day to day and compel the attendance of absent members.
This is a pretty standard provision in state and the federal legislatures. And in the case of Oregon, this Senate rule is really just a formal adoption of something already required in their State Constitution. Article IV, Section 12 thereof states
Section 12. Quorum; failure to effect organization. Two thirds of each house shall constitute a quorum to do business, but a smaller number may meet; adjourn from day to day, and compel the attendance of absent members. A quorum being in attendance, if either house fail to effect an organization within the first five days thereafter, the members of the house so failing shall be entitled to no compensation from the end of the said five days until an organization shall have been effected.
As a bit of a curious aside, the Senate Rules also specifically mandate attendance, but specifies no particular consequences for violations. Section 3.10 (1) says:
(1) A member shall attend all sessions of the Senate unless excused by the President. The Journal will record on each roll call all members “present,” “excused,” or “absent.”
Given the absence of a quorum, no business other than adjourning and compelling absent members can be undertaken anyway. So no punishment for poor attendance could happen internal to the Senate beyond that until a quorum is achieved.
Enforcement of compelled attendance would usually be carried out through police-like forces specifically under the employ and control of the legislative chamber. In this case the Governor stepped in and authorized State police to search for the absent senators and force their attendance. The legal authority for doing this is contained in ORS 181A.090 of Oregon law, which asserts:
The state police, with the approval of the Governor, may be called upon by any other branch or department of the state government to enforce criminal laws or any regulation of such branch or department.
Therefore the Senate, in exercise of its constitutional authority to compel attendance when lacking a quorum, invoked ORS 181A.090 to obtain assistance from the state police, and the Governor consented.
However, the Oregon police and Senate have no authority outside of Oregon. As the Senators had not broken any laws in the State(s) they were hiding in, nor any Federal laws, there was no legal basis for those other states (or the federal government) to arrest them. And in any case they would likely be loathe to extradite them to Oregon against their will, as that's essentially asking one state to intervene in the internal political matters of another state.
In principal, absent Senators could have been recalled and new ones voted in. But this would have taken much longer than the remainder of the legislative session, and it seems likely that they would have been replaced with other Republicans who were likely to be sympathetic to the cause and would continue to not attend while the issue remained active. Support from the constituencies of the absent Senators seemed more than adequate to guarantee this.
As the only way to amend Oregon's constitution, given in Article XVII thereof, starts with approval by both legislative chambers, there's nothing that can be done if a party simply adopts the convention to never attend so long as it would deny a quorum, other than simply waiting for the political landscape to change enough that the people who previously supported this endeavor to change their minds and demand they return or elect Senators that will attend.
