You don't need to read them in any order.
The interesting thing about The Hardy Boys is that the writing style has changed over time. I don't know just how many ghostwriters have been used since their beginning in 1927, but it's got to be quite a few (Wikipedia suggests it's more than a dozen, often collaborating). Combine that with the fact that America itself has changed, and you see that the overall dynamics of the pair and of the plots are far from regular. Nowadays, some of their books have them fighting terrorists. That would not have been happening 60 years ago.
There have been several subdivisions of all the books that have been written. My argument is that most divisions, from a pure reading point of view, are superficial compared with the overall trends. You don't have to worry about reading, say, the entirety of Undercover Brothers to move on to the next period.
- Pick a point and start there. In general, read from that point forward in time, but feel free to jump backwards and forwards.
- Try not to read one book that's more than, say, twenty years older or younger than the last one you read if you care about style. Over that time, it will have changed - a lot - as will the overall story arc.
- Each book is largely self-contained. You'll know most of what you need to know just by reading it cover-to-cover.
Your only problems could really come if you drastically jump around - and that won't impact your consumption of an individual book's plot. However, you'll be a little bit confused at how the story arcs have evolved.
I grew up in the 2000s, reading the revisions of the original series. The revisions probably dated back to the 1970s or 1980s, if I remember correctly. I started at The Tower Treasure - the first one - and got maybe 20 books in. I thought the continuity was rather smooth. There were a few inter-book references, but I didn't have to remember all the details of the previous one.
I then made a jump to one of the newer books, and it was a bit of a shock. The style was very different, and the plot had changed from some small-scale crimes to pretty heavy stuff. I regret having taken that chronological jump; it made me lose interest in the series a bit. Thinking back, I may have gone to the Undercover Brothers series, actually, which deals with much more delicate and violent material. The first one I read contained a car bomb as a plot point, which was a bit shaky for 10-year-old me. It was not a wise choice to make that switch.