Your life is likely to be very long. There is plenty of time for learning ALL those instruments, if you wish. But FIRST, learn one or two instruments REALLY well. I started on saxophone in 6th grade (well-trained in school and by private instructors), picked up flute as a double in college (self-taught), stopped playing for many years, and then picked up tuba and bass trombone (self-taught) in my mid-40s. There is time. Focus first, and branch out later. Become a muscian, and not just somebody who can get sounds out of a bunch of different instruments.
Concerning the tuba, you should easily be able to play one. In fact, given that you play euphonium, you should be able to sit down with a BBb tuba and be able to play it passably in band in probably a week. The fingerings are pretty much the same (some minor differences in different octaves because of where the partials lie since the instruments are an octave apart). Of course, we don't know what kind of "tuba" you tried or what mouthpiece you used. If it was a sousaphone or you used a mouthpiece that is too large (many players do, and are often provided with poor mouthpiece choices by instructors who aren't tuba players), that might explain it. Or if the tuba is leaky or otherwise in wonky shape, that might explain it. But you definitely should be able to play it in the euphonium range without difficulty.
On the other hand, I don't really consider the tuba to be a true "orchestral instrument". So I don't think that right now it would provide you with what you're looking for.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)