Overstayed my US visa for over 10 years, never got deported, can I return as a tourist?

From the information you have provided, you most likely have no ban. But not having a ban does not mean you will be able to get an ESTA/visa, or be allowed to enter the US.

The ban that is relevant here is the INA 212(a)(9)(B) ban where if you accrue 180 days / 1 year of "unlawful presence" and the leave the US, you trigger a 3 year / 10 year ban, respectively. The question is whether you accrued any (and if so, how much) "unlawful presence" before you left the US. The definition of "unlawful presence" is highly technical and is what matters here.

You were in J-1 status, and people entering on J-1 are usually admitted for "D/S" (Duration of Status) on their I-94s, rather than a date. You said you believe it was "D/S" (you should check to make sure); for the purposes of this answer we will assume that it was "D/S".

The USCIS Adjudicator’s Field Manual Chapter 40.9.2(b)(1)(E)(ii) (on page 76 of this PDF) deals with what can trigger "unlawful presence" to start accruing for someone admitted on "D/S":

(ii) Nonimmigrants Admitted for Duration of Status (D/S). If USCIS
finds a nonimmigrant status violation while adjudicating a request for
an immigration benefit, unlawful presence will begin to accrue on the
day after the request is denied. If an immigration judge makes a
determination of nonimmigrant status violation in exclusion,
deportation, or removal proceedings, unlawful presence begins to
accrue the day after the immigration judge’s order. It must be
emphasized that the accrual of unlawful presence neither begins on the
date that a status violation occurs, nor on the day on which removal
proceedings are initiated. See 8 CFR 239.3.

From your description, it seems you were never in removal/deporation proceedings, and you never applied for any benefit to USCIS during the time after your program ended, and furthermore it doesn’t seem like you ever received a formal finding of status violation.

The Department of State Foreign Affairs Manual describes it similarly:

9 FAM 302.11-3(B)(1)(b)(2):

b. (U) DHS has interpreted "period of stay authorized by the Secretary
of Homeland Security," as used in this context, to include:

[…]

(2) (U) For individuals inspected and admitted for "duration of
status" (DOS), any period of presence in the United States, unless
DHS, an IJ, or the BIA makes a formal finding of a status violation,
in which case unlawful presence will only being to accrue the day
after the formal finding is made;

9 FAM 302.11-3(B)(1)(d):

d. (U) For persons who have been admitted for duration of status (DOS)
(as is usually the case with aliens in A, G, F, J, and I visa status),
unlawful presence will not accrue unless DHS, IJ, or the BIA finds a
status violation in the context of a request for an immigration
benefit in the course of a removal proceedings. This finding of
status violation by the DHS, an IJ, or the BIA will cause a period of
"unlawful presence" to begin. In DOS cases where DHS or an IJ or the
BIA makes a formal status violation finding, the alien begins accruing
unlawful presence on the date of the finding (i.e., the date the
finding was published /communicated. […]

With that said, just because you don’t have a ban doesn’t mean you will be able to get an ESTA/visa (when you said "I’m living in a European country now, and I no longer need a visa to enter the US", you mean that your country of nationality is part of the Visa Waiver Program; but you will still need an ESTA to go to the US on VWP if you arrive by air), or be allowed to enter the US. They will likely know about your period of overstay in the US, and if asked on any form about past overstaying or violating the terms of your visa, you must truthfully say yes and provide details. With such a history of long overstay, you are very likely to be denied an ESTA or visa, or be denied entry to the US if you make it there. Even people with perfectly clean immigration histories (or no histories) are regularly denied US visas; with a history of overstay like yours, it will be even harder. However, you are free to try; it is not impossible for you to get it.

UPDATE

Seek legal opinion. There is a school of legal thought which says aliens do not begin to accumulate illegal presence upon termination of SEVIS because it does not constitute a formal finding of violation of status.

Several other legal professionals assert SEVIS termination begins the accrual of illegal presence.

Can I return as a tourist Is there any chance I won’t be let in because they know I’ve overstayed? Would Immigration admit me into the country were I to arrive at the border??

Yes you can return however I would strongly suggest you forget it for another few years. For now your friends could visit you where you are or maybe you could meet in a third country, like Canada or Mexico. Not getting arrested, not being deported and paying taxes doesn’t change the penalty. If your I-94 did not have D/S but a specified validity date and you went beyond it by more than a year, then you triggered the ten year bar for overstaying more than one year when you exited. If it did have D/S, you didn’t accumulate illegal presence however if your SEVIS was terminated (which it likely was if your sponsoring agency is competent), you likely started accruing illegal presence and face the ban.

Module 6: Closing Out Student Records

When you terminate a student’s SEVIS record, your school is no longer
responsible for monitoring the individual unless you request a data
fix on the record or you recommend reinstatement. In these two cases,
you are still responsible for maintaining the record and reporting on
the student. If you do not request a data fix or reinstatement for a
student with a terminated SEVIS record, you should let the student
know that he or she must depart the United States immediately.
Students who do not leave may accrue unlawful presence and may be
barred from reentering the United States.

You will be eligible to return to the USA ten years after you left. I will advise you to get a visa before coming at that time because you are very likely to be denied entry if you attempt entering on VWP. Of course you could file for a waiver however from your statements you don’t qualify.

Consequences of Unlawful Presence in the U.S.—Three– and Ten-Year Time Bars

Three Years

If you spent more than 180 continuous days (approximately six months)
in the U.S. unlawfully and then left voluntarily (before being caught
and placed into removal proceedings), you could be barred from coming
back for three years.

Ten Years

If you spent more than one continuous year in the U.S. unlawfully, and
then left for whatever reason (including being deported), you could be
barred from coming back for ten years.

ALIENS UNLAWFULLY PRESENT

Under section 212(a)(9)(B) of the Act, an alien is inadmissible if the
alien has accrued a specified period of unlawful presence, leaves the
United States after accruing the unlawful presence, and then seeks
admission during the period specified in (either 3 years or 10 years
after the departure, depending on the section 212(a)(9)(B)(i) duration
of the accrued unlawful presence).